731. k
Bairstow
Countpoint and Harmony
781.4 B16
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COUNTERPOINT AND HARMONY
COUNTER&f j| AND
HARMONY,
EDWARD C. BAIRSTOW
LITT. D., Mus. D, ( F.R.C.O.
PROFESSOR OF Music AT THE UNIVERSITY OF DURHAM
MACMILLAN AND CO,, LIMITED
ST, MARTIN'S STREET, LONDON, &
STAINER AND BELL, LIMITED
58 BERNERS STREET, LONDON
1937
\
,.
miHT9 IK OKUT IMITAIV Mlf Ol 58
ACKNOWLEDGMENTS
The author thanks most warmly the following who have kindly
given him permission to use copyright tunes :- -
Messrs. Augener, Ltd.
A Lawyer he- went out one. day (from English Folk Songs, arr. by
George. Butterworth).
(Section XI, Exercise !)).
Messrs, J. B. Cramer & Co., Ltd.
The Gentle Maiden and The Castle of Dromore (from Songs of the
Four Nations, ed. by Harold Boulton, the music arr. by Arthur
Some well).
(Section VII, Exercises 10 and 20).
Messrs. Enoch & Sons (1927), Ltd., and Mr. Herbert Hughes.
Irish tune, Open the door softly.
(Section XV, Exercise 4).
Messrs. Methuen & Co. Ltd.
Matthew, Mark, Luke and John (from Songs of the West).
(Example 227).
Messrs. Novello & Co. Ltd., and Miss Karpeles, Executrix of the
late Mr. Cecil Sharp.
Banks of the meet Dundee (Example 153).
The Crystal Spring (Example 154).
Sovay, Novay (Section IX, Exercise 0).
Henry Martin (Section IX, Exercise 10).
Gently, Johnny my jingalo (Section IX, Exercise 27).
Searching for Lambs (Section IX, Exercise 28).
Seventeen come Sunday (Section XI, Exercise 7).
The Sonny Bunch of Roses (Section XI, Exercise .8).
A Lawyer he went out one day (Example 326).
All the above arc taken from Mr. Cecil Sharp's Collections of English
Folk Songs
Messrs. Novello & Co., Ltd.
Two quotations from The Dream of Gerontius, Klgar. (Examples
J61 and 463).
Miss Karpeles.
English Traditional Melody, The Unquiet Grave (English Hymnal).
(Section II, Exercise 20.')
Oxford University Press.
Czech Carol (Example 228).
The righteous Joseph (Example 220).
English Carol (Section XI, Exercise 1).
Lullaby of the Nuns of Chester (Section XI, Exercise 5).
ACKNOWLEDGMENTS
Irish Folk Tune (Section XI, Exercise 6)j,
Netherlands Traditional Tune (Section XI, Exercise 13).
The above are taken from the Oxford Book of Carols.
Messrs. Stainer & Bell, Ltd.
Joseph and Mary (Example 22(5).
English Traditional Carol (Section XI, Exercise 12).
Ancient Irish Hymn-tune, St. Columba (from the English Hymnal).
(Section XVII, Exercise 6.)
Quotation from No. 1 of Five Mystical Songs, Vaughan Williams,
(Example 400 (b)).
Dr. R. Vaughan Williams, O.M-.
/ will give MI/ love an apple (Example 230).
Glencoe (Section XI, Exercise 14).
If by mischance any copyright tune has been included without
permission, the author makes his humble apologies.
His best thanks arc given to Miss Valerie Selby for unstinted help
and advice, and to Dr. Ernest Bullock for a careful revision.
ABBREVIATIONS
C.F. = Canto Fermo.
Ex. = Example.
Paragraphs are referred to by numbers in brackets, e.g. (100).
Intervals are indicated by Arabic numerals, e.g., 6th the interval of
a sixth.
Chords are referred to by numerals printed in full, e.g., Sixth * the
chord of the sixth.
Degrees of the Scale are indicated by Roman numerals, e.g., vii * the
leading-note.
VI
CONTENTS.
ABBREVIATIONS USP:D IN THE TEXT
INTRODUCTION -
PAGE
vi
- ix
PART I. STRICT COUNTERPOINT AND CONTRAPUNTAL HARMONY
SECTION I Two-part counterpoint, note against note.
The First Species of strict counterpoint - 1
SECTION II Adding a bass to a simple melody - - 29
SECTION III Modulation 45
SECTION IV Adding a melody to a given bass - - - 55
SECTION V Three-part work in the First Species - - 61
SECTION VI Two notes against one. The Second Species of
strict counterpoint 60
SECTION VII The Second Species applied to melodies and
basses 87
SECTION VIII Suspensions, The Fourth Species of strict
counterpoint 104
SECTION IX Four-part writing - - - - 117
SECTION X Suspensions in XVIth century counterpoint * 147
SECTION XI The Modes 184
SECTION XII The Third Species of strict counterpoint - 238
SECTION XIII The Fifth Species of strict counterpoint - - 246
PART II. DIATONIC DISCORDS^-
SECTION XIV The second inversion of triads, the chord of
the Dominant Seventh and its inversions - 256
SECTION XV The chords of the Ninth, Eleventh and
Thirteenth - - - - - - 270
SECTION XVI The Dissonant Triads and Diatonic Sevenths 303
SECTION XVII Free Counterpoint
- 314
PART III. CHROMATIC HARMONY-
SECTION XVIII Chromatic Passing Notes
SECTION XIX
SECTION XX
SECTION XXI
Chromatic Triads
Chromatic Discords
Chromatic Appoggiaturas
Counterpoint -
and
- 345.
- 351
- 363
Chromatic
- 384
vn
INTRODUCTION.
IT was Sir Charles Stanford who suggested the compilation of this
book. It was his idea that the study of counterpoint and harmony
should be simultaneous. He it was who proposed that the modes
should be fully explained and exercises given in modal counterpoint.
An attempt has been made to arrange the matter in such a way as to
enable students to write modal counterpoint as soon as possible without
a semibreve Canto Fermo. The author is convinced that, for the
majority of students, the order followed in the book is the best. It may,
however, be found more expedient for some who, for examination or
other purposes wish to acquire a knowledge of Third and Fifth species
of counterpoint, to study Sections XII and XIII before the freer and
more beautiful XVIth century type treated in Sections X and XL
Or, for similar reasons, the six-four chord and the dominant seventh
can be learnt as soon as the student has the ability to write easily in
four parts. But a long experience of teaching has convinced the .author
that it is best to deal out technique in small doses and give reasons for
rules where that is possible. People naturally rebel against learning
anything for which they cannot understand the reason, and from whiqh
they do not see much hope of profit. Moreover, if their minds are
directed into one channel and all others are kept closed for a time,
they have no distractions and are taught economy by being encouraged
to produce beauty from slender resources. It goes without saying that
the acquisition of line, shape and movement in part-writing is of far
more importance to the beginner than the knowledge of harmonic
colour. The chronological sequence also is then more or less preserved.
In these days it is vital that young musicians should know what their
forefathers did, and when they did it. They can then see the logical
development of all that is good in modern music and reject the ugly,
dull stuff that is put forth by composers whose music contradicts the
sound principles of all the great masters. It is for these reasons that
only the harmony of XVIth century counterpoint is permitted until'
Part II is reached, and that chromatic harmony is not dealt with until
Part III.
A book of this kind must be so constructed as to be of service to all,
from the executant, who has to learn a little harmony and counterpoint
to gain a diploma, to the embryo composer. Sufficient exercises are
therefore given on each subject to enable those who are not specially
gifted or interested in counterpoint and harmony to obtain facility
before they proceed to the next. Some, of course, will arrive at this
stage before they have worked out all the exercises. The exercises
themselves have been made interesting by using fine tunes wherever
this was possible, and by giving exercises in pianoforte writing.
ix
X INTRODUCTION
Here it may be said that drawing from a model can never teach the
composition of a picture. In other words, working out counterpoint
and harmony exercises is of no use to show " what comes next " in a
movement of absolute music without words. It will merely help by
removing the distraction of part-writing, but it will do no more than
that. It is therefore strongly recommended that composition be studied
and practised from the first moment this is possible, namely by writing
original "tunes as soon as Section IV is reached. Stanford's plan of
making students write " over " a classical model has been adopted in
this book as far as counterpoint is concerned. As soon as students
have developed sufficient skill in part-writing, they can carry out this
plan in composition by first of all taking as a model a short Minuet or
Scherzo by Haydn, Mo/art 91- Beethoven. Only the form should be
copied the length of the phrases, the modulations, and above' all the
rhythmic contrasts and development of themes. The rest themes,
harmony and rhythmic divisions must be original work. This may
be commenced when Section XVI is reached. Afterwards, longer
movements may be attempted.
One more point must be mentioned here. There has been a tendency
in this country to teach counterpoint and harmony in such a way that
students became stiff, cramped and unimaginative in their work.
They were not encouraged to use their ears and their common sense,
but were merely told that certain things were wrong and must be
avoided. The author devoutly hopes tha.t the study of this book will
produce freedom and ease. General principles have therefore been put
before " rules." The view has been adopted that nothing is " wrong "
or " right," but that if rules are observed, smoothness will result no
more and no less. The fact has also been stressed that nothing can be
decided by one consideration only. Several factors must be brought to
bear on every problem to be solved, the most important in every case
being movement the horizontal, not the vertical aspect.
There is infinite variety in people's powers of observation. They
vary in proportion to interest and enthusiasm. If everyone was perfect
in this respect, and if everyone was acquainted with the best repertory
of music from Palestrina to the present day, text-books on counterpoint
and harmony would be unnecessary. Those who have eyes to see and
ears to hear will have observed many of the things explained before
they study them in a text-book. But many more will not have done so.
The former must be patient if they are obliged to wade through matters
obvious to them. The latter must take a deeper interest in music and
verify at first-hand the principles they learn from the text-book.
PART I.
STRICT COUNTERPOINT AND
CONTRAPUNTAL HARMONY
SECTION I.
TWO-PART COUNTERPOINT, NOTE AGAINST NOTE.
THE FIRST SPECIES OF STRICT COUNTERPOINT.
1. Counterpoint is the art. of writing one or more melodies, or
counterpoints, against a given melody, or Canto Fermo (/.<?,, iixed song).
2. Harmony teaehcs the knowledge of chords (three or more
simultaneous sounds) and the art of joining them together so that they
sound coherent and smooth.
3. In the First Species of counterpoint, the student has to add one
part either above or below the Canto Fermo (C.F.), each note of the
counterpoint being of the same length as that of the C.F. To do this
there are certain considerations connected with intervals which must
be fully understood. These considerations divide themselves into two
classes, vertical or harmonic, and horizontal or contrapuntal.
4. The harmonic considerations are to ensure that the intervals
between the C.F. and the counterpoint will not clash, and will have such
bearing on, or relationship with, their neighbours that coherency and
smoothness will result.
5. The contrapuntal considerations are to prevent the counterpoint
jumping about aimlessly, or moving so little that it becomes dull and
uninteresting.
Vertical, or harmonic considerations.
6. *The intervals allowed vertically in this species in two parts are
as follows :
All the perfect consonances with the exception of the 4th.
All the imperfect consonances.
# It is taken for granted that those who use this book have already acquired a knowledge
of the harmonic names of the degrees of the scale, the numerical and qualifynifi M times of
the intervals, and can hear what they write. The hook is of no use M an inttrtthird ear,
B
COUNTERPOINT AND HARMONY
7, The 4th is not considered as a consonance when it occurs between
any part and the bass. In this case, it very slightly partakes of the
character of a discord, that is, it requires to be followed by some other
interval to complete the sense, and is therefore not quite so independent
and self-sufficient as the other consonances (Ex. 1). Let us consider
the intervals singly and in detail.
Ex.l
8. The Unison, where two parts sing the same sound simultaneously,
is a perfect consonance, and, like other perfect consonances must not
be used consecutively (18), It is so thin in effect in two parts that it
must appear infrequently. Its best use is at the first and last bar of
the C.F., or phrase -the tonic or dominant at the first bar, and the
tonic at the last (Ex. 2).
Ex, 2
C.F.
IE
*=5=-
O-
Ml
^
r
TTCI I
o
O' 1 "
*
'*" ""
O" ".-
i :7:,ii" i ::;:;;i
'-"My :"""_
~- tar""-
J3I_
*
^ *x ^
CLF.
0. The Major and Minor Third are imperfect consomuwes which
may be used freely and consecutively. A string of more than three
would be monotonous, and would lessen the independence of
movement between the C.P. and the counterpoint (Ex, 8). This applies
to all imperfect consonances.
Ex. 8
10, The Perfect Fifth is another perfect, consonance aud, like the
unison, must not be used consecutively. It must be used sparingly
in two parts on account of its extreme consonance and consequent
dullness,
11. The Major and Minor Sixth are imperfect consonances which
rmi be used freely, but a succession of more than three is monotonous
(Bx, 8),
FIRST SPECIES IN TWO PARTS 3
12. The Octave is a perfect consonance which, like the unison and
fifth, has no major or minor quality. It must not be used consecutively,
and should not be frequently employed in two-part counterpoint.
J 13. The more consonant the interval the worse the effect when
used consecutively. Unisons and 8ths simply reproduce the same
sounds. Consecutive 5ths come next in order of consonance. A scale
of perfect 5ths is monotonous because all the intervals are perfect
consonances except the 5th on the leading note (Ex. 4 (a) ). A scale
of 3rds or Gths varies between minor and major (Ex. 4 (b) and (c) ).
A passage like that shown in Ex. 5 is harmless in effect, but is purely
harmonic, not contrapuntal.
Ex.4
..U. !-' - ..,.
r
i O j
i n
(fa O
Perf.
*=
Perf.
Perf.
Perf.
Perf.
Perf.
Dim.
Perf.
*
o
e
(b)
*
~_.
CT
o
9=^=
n
Min.
e- 1
Min.
Maj.
Maj.
Min.
Min.
Maj.
r -j-^
-i "I 1 -,.
I" 1 :.:* 1 !, 1 : 1 :"l
"* r
i "~
7t*
^g
o
ui
i?
P it Min '
Maj.
Maj.
Min.
Min.
Maj.
Maj.
Min.
M)
_
e
Ex.5
=lfc
A perfect consonance remains perfect when inverted. An imperfect
consonance changes from major to minor, or vice versa, when inverted.
A perfect consonance becomes a dissonance when augmented or
diminished by a semitone. An imperfect consonance, after the sub
traction or addition of a semitone, changes from major to minor, or
vice versa, but still remains a consonance. In fact, whatever is true of
the perfect consonance is untrue of the imperfect consonance, except
that both are consonant. The student will gather from this that as the
perfect and imperfect consonances are so different in effect, it is only
4 COUNTERPOINT AND HARMONY
natural that they cannot be used indiscriminately, or be governed by
the same rules.
Triads and their inversions.
14. As a child first learns to read words familiar to it by sound, so
the student of harmony begins by learning to give names to the simplest
chords which have been heard and played many times.
A Triad is the combination of any sound "with the 3rd and 5th
above it.
A major triad has a major 8rd and a perfect 5th.
A minor triad has a minor 3rd and a perfect 5th.
A diminished triad has a minor 3rd and a diminished 5th.
An augmented triad has a major 3rd and an augmented 5th.
15. In Ex. 6 chords (a) to (d) are all triads of C major, for in each
case C is the lowest note, E is the major 3rd above it, and G the perfect
5th. Chord (e) is the triad of D minor, the 3rd, F, being a minor 3rd
above D, the root. Chord (/) is the same triad with the 5th, A, appearing
twice in it. In (e) D, the root, which appears twice, is said to be
" doubled." In (/) the 5th is " doubled." Chord (g) is the major
triad of G, (h) is the ttiajor triad of F. The example at ( j) is the
diminished triad of B, for D, the 3rd, is minor, and F, the 5th, is
diminished, (A*) is also a diminished triad, whilst (/) and (m) are aug
mented triads, for in each case the 3rd is major and the 5th augmented.
Ex.6
(c)
W (j) (k) (I) (m)
BE
O
xc
3DC
16. When the 3rd of a triad is in the lowest part, the chord thus
formed is saicl to be the First Inversion of a triad. The first inversion
of a major triad is the combination of a sound with the minor 3rd and
minor 0th above it, and that of a minor triad the combination of a
sound with the major 3rd and major 6th above it* Thus in Ex. 7 (a),
as the notes forming the chord are C, E and G, it must be some form of
the chord of C. But as E, the 3rd, not C, the root, isr the lowest, or bass
note, it is said to be the first inversion of the triad of C major ; the
interval E to G being a minor 3rd, and the interval E to C a minor 6th.
Similarly (b) is the first inversion of the triad of E minor, G to B being
a major 3rd, and G to E a major 6th. In this example the root, E, is
doubled. Chord (c) is the first inversion of G major ; (d) is the first
inversion of the diminished triad of B. It is the combination of a
minor 3rd and a major 6th above the bass note D. Chord (e) is the
first inversion of an augmented triad.
17. The diminished and augmented triads arc not used in strict
counterpoint. They would involve dissonant intervals with the bass
((6) (7), and Ex, 6 (j) to (m)). The first inversions of the diminished
Thi Triad is in its Second Inversion when the Sth is the lowest note,
FIRST SPECIES IN TWO PARTS ' 5
triads are used freely. The dissonance between the two upper notes
(F to B in Ex, 7 (d) ) is considered slight enough to warrant this. There
is no dissonance with the bass. The first inversion of the augmented
triad (Ex. 7 (e) ) is not used, the diminished 4th between the two upper
notes partaking so strongly of the nature of a dissonance that it would
require a definite resolution, that is, a chord following it to complete
the sense.
Ex.7
o (a}
Jt
(b)
T r
(c)
1 8 1
(d)
(e)
r-Wi n
% .
*> n
o~
ft
*
Implied chords.
18. A musical person, even without any knowledge, imagines
mentally some harmony to accompany single sounds or intervals when
he hears them. Such sounds also imply to him a key. This can easily be
proved by playing a sound and then asking him to sing another, foreign
to the key of the first. For instance, lie will readily sing B if he has
first heard C, but finds it difficult mentally to hear B flat. Likewise,
if a simple succession of sounds is played for him, such as Ex. 8, and he
Ex.8
is asked to supply the harmony, he will play some primitive succession
of chords such as this :
Ex.9
8
s
It is this faculty the mental conception of sounds upon which the
writing of music depends. It can be developed by using it constantly
until a complicated orchestral score can be Heard mentally.
19. The mental ear will cbntinue to imply any chord that has been
thoroughly established until another has been equally well fixed.
Thus, in Ex. 10 (a) the interval Bfr D, implies the triad of B[? major,
for that triad has been thoroughly established by the two previous
intervals. But the same interval in Ex. 11 (a) implies the first inversion
of the triad of G minor for the same reason. The student should play
on the piano the first three intervals in Ex. 10 with the sustaining
pedal depressed, and then immediately do the same with the first three
intervals in Ex. 11. Likewise, Ex. 10 (b) implies the triad of F major
t5 COUNTERPOINT AND HARMONY
established as the dominant of the key of B|j by what has preceded it ;
but the same two sounds in Ex. 11 (b) imply the first inversion of the
triad of D minor. Ex. 10 (c) implies the second inversion of the triad of
Bj? major, for it is sandwiched in between the other two positions of
that chord, and therefore the mental ear will not accept it as the first
inversion of the triad of D minor> the only other possible chord from
which it might be derived. Second inversions are not used in strict
counterpoint until the Fourth Species, for they very slightly partake
of the character of discords, one of the upper notes making the interval
of the 4th with the bass or lowest note (7). This instinct for the implied
chord, far from being a difficult thing to acquire, is found in nearly
everyone who is at all musical. It only needs cultivating. It will
prevent the writing of a. string of intervals all of which imply the same
chord where that would lead to monotony, and will indicate when an
innocent-looking 6th is really an implied second inversion.
Ex.10
pn
?
[ P r f J q
t=
- 1 1
(c) (a) (5)
1 J J 1 =
|m
H
J J J J
_
Ex. 11
(I)
The relationship between the triads,
20. The degree of smoothness with which one chord follows another
depends on three factors : (1) the relationship of one chord with
another ; (2) the character of the motion of the parts, whether similar,
contrary, or oblique, by step or by leap ; (3) the position of the chords
with regard to the rhythm and shape of the phrase* The last two
factors belong to the horizontal considerations which follow. The
first, the relationship of one chord with another, depends on key
relationship, and that depends on the number of notes common to the
scales of which "the roots of the triads in question are the tonics, or
key-notes. Thus the triad of C is most closely related to the triads
of G, F, and A minor, because the scales of G, F and A minor have more
notes in common with the scale of C than with any other scales.
21. If the notes of a major scale are compared with the notes of
the scales beginning on every degree of that scale, including the
harmonic minors and the ascending and descending forms of the
melodic minors, then the following result is obtained, which is here
arranged in order of relationship, the strongest first ;-
FIRST SPECIES IN TWO PARTS
Proportions
6 notes in common with dominant scale
6:7
IT : 21
3:7
6 sub-dominant scale
6 sub-mediant har. minor
scale
5 sub-med. mel. minor
scale, ascending
7 sub-med. minor scale,
descending
The 5 super-tonic har. min.
tonic I scale
scale 6 super-tonic mel. min.
has scale, ascending
6 super-tonic mel. min.
scale, descending
5 ,, mediant harmonic min.
scale
4 mediant mel. min. scale,
ascending
6 ,, mediant mel. min. scale,
descending
22. Other relationships might be worked out in the same way.
But the ear is much the best guide. It is better to rely upon it, and
not upon mechanical substitutes. Bear in mind that the explanation
given above is not to ensure that contiguous chords should always bear
a strong relationship to each other. The cheapest and commonest
music has this characteristic, and continually employs only the tonic,
dominant and sub-dominant triads and the dominant discords for its
harmonic scheme. Any two triads in ju^t,qiQartion may be made to
sound beautiful, but it is the other two factors mentioned at the beginning
of (20) that help towards this.
Doubling the Major 3rd.
23. The mediant and leading note are the two sharpest notes in the
major scale (235). Prove this by playing every C and G on the piano
with the sustaining pedal depressed, then, still keeping the pedal
down, play the middle E. Compare the effect of this with every C
and E played, but only one G ; or every E and G with only one C.
It will be found that, while one E leavens the whole lump, the other
two effects are spoiled by too many E's. A little major 3rd goes a long
Ex. 13
3E
8
COUNTERPOINT AND HARMONY
way. This is explained acoustically by the harmonics, or upper partials
given by the three notes of the triad. In Ex. 12, ivhere the white notes
are the three notes of the triad, and the black ones their first few
harmonies, it will be seen that the harmonics G sharp and B from E,
the major 3rd, clash with the harmonics of the other two notes. This
also explains why major 8rds low down in the bass sound thick and
muddled, for low sounds give more distinct harmonics than high ones,
It is for this reason that the following rule is given :
24. The 3rd of a major triad may not be doubled unless the
character of the motion of the parts admits of it (36).
The leading ipte is the worst of the three to double ; next in order
comes the 3rft of the tonic triad, the mediant ; then the 3rd of the
sub-dominant triad, the sub-mediant.
25, The above rule only comes into two-part counterpoint in two
instances :
(1) when an octave is used and the chord implied is the first
inversion of a major triad ;
(2) when the leading note is in the lower part.
In Ex 1 . 13 (a) the three previous intervals have established the triad
ofjC, therefore (a) is a doubled major 3rd ; (b) is equally wrong because A
is the major 3rd t>f the triad of F, this having been clearly established
by ( jthe preceding bars.
Ex.18
fee. 14 (a) and (b) are instances of a better use of the same two
intervals. At (a) the minor triad of D, and at (b) the minor triad of G
is implied.
26. When the leading note is in the lower part, only one harmony
is available, namely the first inversion of the dominant triad ; for the
leading note triad is diminished and therefore not permissible. Thus
the only possible intervals to use are the minor 3rd and 6th above.
Ex. 15 shows what intervals are available above and below the C.P.
on every note of the major scale. The intervals greater than the
octave are not shown. Ex. 15 must be taken in conjunction with
(24)-(26), as well as (19) (implied 2nd inversions).
FIRST SPECIES IN TWO PARTS
Ex.15
Intervals available above the C.F.
Jf -v
i _-
m , .
fr . . m ==\
m a 1 ": 1 ,, 1 * '" :
w
. ' =
() ()
fj -O"
Intervals available bel
-HI HI
ow the C. P.
A. m
-&
* .
j ~
Tfc '
Z
\w) l^/
$~T^
-e
() ()
1^-- " ffil
1* * ^ - _ 1
1 - . ,
* .
(a} When the mediant is the root of the mediant triad
(b) When the submediant is the root of the snbxnediant triad
Ex.16
Horizontal, or Contrapuntal considerations.
27. These are all matters concerned with the flow, or wave-shape
of the counterpoint. The easiest way to conquer difficulties is to
take them one at a time. It is the multifarious distractions in the
mind of the beginner that cause trouble. To begin with, therefore,
counterpoint is written in the simplest rhythms. The first species
has only one semibreve in each bar, and the first C.F's. consist of only
one phrase with only one cadence (41). It is for the same reason that
the counterpoint is limited as to the intervals by which it progresses,
and is diatonic, not chromatic.
28. The horizontal intervals allowed are all diatonic. They are the
major and minor 2nd, major and minor 3rd, perfect 4th, perfect 5th,
minor 6th and perfect octave. No part may proceed by an augmented
interval, a diminished interval, a 7th, or by any interval greater than
an octave.
29. The leap* of a 7th or 9th is often as jerky in two jumps as in
one (Ex. 16). The tritone, or augmented 4th, is not contrapuntal in
* When a part proceeds by any interval greater than a 2nd, it is said to " leap " ;
when it proceeds in 2nds it is said to move " by step."
10
COUNTERPOINT AND HARMONY
flavour. No part may proceed by it, nor may it appear with one note
intervening when that note lies between the two notes forming the
tritone (Ex. 17). It will be heard when, it forms the crest and trough
of a wave. In Ex, 17 (a) the tritone is noticeable, and also in Ex. 18 (a)
and (t), but not in Ex. 17 (b) or Ex. 18 (c), where the interval of a 5th,
F to C, forms the trough and crest of the wave. After a leap it is
generally best to proceed by step in the opposite direction. This should
always be clone after a big leap such as an 8th or minor 6th (Ex. 19).
If two leaps are made in the same direction, they should be made
through the notes of the same triad, as a 5th followed by a 4th, or a
major 3rd followed by a minor 3rd, or vice versa, or 3rd followed by 4th
ascending, or 4th followed by 3rd descending (Ex. 20 (a) ). If leaps
occur in the course of a passage which otherwise proceeds by step, the
leaps should be small ones, such as a minor 3rd (Ex* 20 (b) ). The
leaps of a diminished 5th and of a major 6th are not found in Palestrina ;
and, as strict counterpoint is a preparation for the study of XVIth
century counterpoint, they should be avoided. They may be used when
adding a part to a melody (end of 80).
Ex, 17
W
nn
Ex.18
(i)
Ex.19
FIRST SPECIES IN TWO PARTS
11
30. Repetition of the same note may be used occasionally in First
Species as Ipng as the repetition dofes not spoil the shape of the phrase.
Length and weight go together in rhythm, so that a long note is always
a heavy and important one. Repetition of two or three notes is bad.
It holds the counterpoint down to one emotional point, and takes
away its freedom (Ex. 21). The frequent return to one sound in the
course of a phrase is bad for the same reason (Ex. 22).
Ex.21
Ex. 22
9 bars with 4 C s, 3 Bs and D'S
Ex.28
ft ( fl )
It
1
-dro o '
& r n
It ^
(c)
(d)
81. A student's first exercises cannot be expected to express deep
emotional thrills. Therefore agitated, jumpy wave-forms would be
ridiculous in them. They can, nevertheless, be given plenty of variety.
Ascent and descent may be gradual (Ex. 23 (a) ) ; ascent may be
sudden and descent gradual (Ex. 23 (b) ) ; or vice versa (Ex. 23 (c) ).
But if both are sudden (Ex. 23 (d) ), then only one wave of this kind
should appear amongst others of more gradual ascent and descent,
otherwise the counterpoint may get too jumpy (Ex. 23 (e)). The
12
COUNTERPOINT AND HARMONY
vertical distance between crest and trough makes all the difference :
if it be great, then what has just been saicl is all-important. Big rollers
often have little wavelets on their flanks (Exs. 24 and 25). Many
other varied examples might be given, but the student should observe
for himself all the good tunes that appeal strongly to him and contrast
them with some Victorian hymn-tune, for instance, where the sugary
effect is entirely produced by the harmony, neither the melody nor any
of the other three parts having much life or shape in them.
Ex. 24
from a
rth Carol
Ex.
Prom the Arfa *Wkere e'er you walk* Handel
82. Motion between two parts is of three kinds : Similar, when both
parts move in the same direction ; Contrary, when the parts move in
opposite directions ; Oblique, when one part is stationary and the other
either approaches it or recedes from it. Of these three, Contrary Motion
best exhibits the true spirit of counterpoint, that is, the art of writing
independent melodies. The parts may be independent when they arc
in Similar, or Oblique Motion, but in Contrary Motion they mmt be.
Exposed perfect consonances.
83. These occur when both parts (or the outside parts when there
are more than two) approach a perfect consonance by similar motion,
and thus accentuate the hard, bare character of those intervals; They
used to be called u hidden consecutives " on the supposition that the
bad effect if there happened to be one was caused by the ear supplying
the unessential notes filling up the intervals by which the parts leaped
and thus causing implied consecutives. In Ex. 26 the small notes are
those supposed to be implied by the mental ear. This is a false
explanation. The theorists who used it all allowed certain excep
tions where the effect was considered good, but there is no reason
why the ear should not imply the unessential notes in every ctoe,
exceptions included. No trustworthy explanation of the bad effect
which may occur in these cases can be given which rests cm one factor
only. ^Che three factors to be considered are those mentioned in (20),
namely : (1) the relationship of the intervals, or chords ; (2) the
character of the motion, that is, by step or by leap ; (3) the position of
the perfect consonance as regards the shape of the phrase and the
rhythm. When the leap of a big interval is made it tends to accentuate
the sound or sounds to which the leap is made*^ This, like most things
in music, is perfectly natural One comes to earth with a bigger bump
after a long jump than after a short one, after a high one than after a
low one. VThe more parts there are leaping in the same direction the
stronger the accent at the end, \It two parts move by step to a perfect
consonance the result is f of course; conseeutives ; a leap of some sort,
therefore, in one of the parts is a foregone conclusion. \ With regard
FIRST SPECIES IN TWO PARTS
18
>to the rhythm, the character of any note, interval or chord is accen
tuated when the leap is from a weaker to a stronger note, and lessened
when the opposite is the case.
84. The following table, comparing relationship with motion,
together with Ex. 27, should make the foregoing clear :
Relationship. Motion. Effect.
1. Close. One part by step the other by leap. Harmless,
Both parts by leap.
2. Close.
Distant.
Distant,
One part by leap the other by step.
Both parts by leap.
Rather ugly,
avoided.
Uglier, avoid.
Very ugly.
best
85. Considering that there are nine different intervals by which
either part may leap up or down, and thirty different juxtapositions
of the six triads to say nothing of their first inversions and that the
permutations and combinations of these will all produce different
effects, it will be readily understood that, as was said in (22), the ear
must always be the final arbiter.
Ex. 36
o
J^
e
ft v
\
1 \
o <)
e
Ex. 37
86. It was stated in (82) that Contrary Motion fulfills the spirit of
counterpoint better than either Similar or Oblique Motion. It also
Ogives far more variety in intervals. With it there can be no real
consecutives. Consecutives by contrary motion, or unisons proceeding
'"""to octaves, have nothing like so pronounced an effect, but they sound
flQthin in two or three parts. The relationship between the chords matters
'very little when the parts are in contrary motion, and still less with
contrary motion by step. Doubled major 8rds and even leading notes
sound quite harmless under these conditions (Cp. Ex. 81, Bass -anti
oprano of 2nd and 4th phrases). Exposed perfect consonances cannot
oocur in contrary motion.
_j 87. When the relationship between adjacent triads is strong, exposed
-n perfect consonances and even real consecutives have practically no bad
^ effect whatever. Familiarities,, accepted and acceptable between the
members of a family, are not appropriate or tolerable between strangers.
14
COUNTERPOINT AND HARMONY
Such progressions as in Ex, 28 are common enough in composition.
They must not, however, be written in ignorance. That is why the
beginner is debarred from using them;
Ex.38
I 8
J J-^,^ ,j -
8
^^ ||
j
i
Ff^-
4-
f
5
-4
1"^ "
L IP^^,. *-l
^t=J
Overlapping of the parts.
38. An overlap is said to take place either when the lower of
two parts moves to a note higher than that sounded previously in the
upper part, or when the upper of the two moves to a note lower than
the one sounded immediately before in the lower part (Ex. 29).
39. Overlaps have no bad effect except
(1) when they interfere with the clearness of the part writing,
that is, when they leave any doubt in the hearer's mind as
to which note was sung by either, or both parts. Thus,
in Ex. 29 (a\ the F sharp has such a strong tendency to
progress to G that the ear naturally implies that the part
which sang F sharp also sings G. In that particular case,
therefore, it would be clearer to cross the parts as at (i) ;
(2) when they cause jerks instead of waves'. In Ex. 29 (c) the big
dive in similar motion by both parts has more to do with
whatever bad effect there is than the actual overlap itself ;
(8) when they come between chords, or implied chords, which are
unrelated, or distantly related. When the chords, or implied
chords, are closely related, as at (d) and (e) 9 there is no bad
effect in the overlap. When the parts move from one
position of the same chord to another no evil result can
accrue (Ex. 29 (/) ).
Ex.29
(d)
(f)
Jrf
^,
-.
-jJL
~~
ixscn
t^
^^
/
\
\
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1
.
1^
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Ex.80
Amrio
FIRST SPECIES IN TWO PARTS
15
Grossing the parts.
40. The parts may occasionally cross when such crossing improves
them. Simple as is Ex. 30 by Anerio, the beauty of it is amazing.
Crossing and overlapping should be used as a source of beauty and
variety, not as a means of escape from difficulty.
Cadences.
41. Cadences are music's marks of punctuation. A cadence is made
by the juxtaposition of two strongly related chords, or implied chords.
If the chords are as strongly related as possible dominant followed by
tonic, or sub-dominant followed by tonic the result is a musical full
stop. The dominant-tonic cadence is termed a " Perfect Cadence,"
and that between sub-dominant and tonic a " Plagal Cadence " (142).
If this full stop is in the principal key, then the music is at home amongst
the family. If the full stop is in a related key to which the music has
modulated, then it has, so to speak, paid a visit to the abode of some
old friends who live close at hand ; if in some distant key, then the ex
cursion is to the residence of more or less strangers. When the dominant
chord is preceded by the tonic, or some other related chord, the cadence
is said to be a " Half Cadence," like a semi-colon, or colon. The friend
has been met in the street ; we shake hands with him and pass on.
If the final chord is in its original position, but the penultimate is an
inversion, the effect is not so final as when both chords are in their
original positions. When both are inversions only the smallest comma
is perceptible we only nod to the friend without stopping to speak.
These cadences are called " Inverted Cadences." If the music seems
to be making for a cadence but, when it should arrive, the dominant
Ex.31
J. JJ fi
From Andern&ch Ges&ngbuch. 1608
(w
H*
i
f
r r
T: r
^
^
w
&
TT
1AA
rr
^
r r
n 9 "^
T
16
COUNTERPOINT AND HARMONY
chord is followed by some chord other than the tonic usually the
sub-mediant the cadence is termed an " Interrupted Cadence."
We knock at the door, but there is no one at home.
42. In Ex. 81, a German tune of the XVIth century, (a) is an
Inverted Perfect Cadence ; (b) is a Plagal Cadence ; (c) is an Interrupted
Cadence ; (d) is a Perfect Cadence. The two different versions of the
second phrase of the tune which follow end with (e) a Half Cadence,
and (/) a Perfect Cadence in a related key the dominant, A.
Sequences.
48. A Sequence is the reiteration one or more times, at a higher or
lower pitch, of a phrase or the section of a phrase.
If each horizontal interval is exactly reproduced the Sequence is
said to be a Real Sequence. If the numerical measurement of the
intervals is reproduced (2nd, 3rd, 4th, etc.), but their qualifying
characteristics (major, minor, etc.) are allowed to vary with the position
of the reiteration in the scale, the Sequence is said to be a Tonal
Sequence.
Ex. 82 (a) is a Real Sequence. There are four notes in the section
reiterated, the intervals between which are minor 2nd, major 2nd,
major 2nd. The interval between the section and its reiteration is a
minor 3rd. These are all reproduced with each reiteration. In
Ex. 82 (b) the same notes are reiterated, but the Sequence is kept in the
scale of G and the intervals, therefore, differ with each reiteration.
This is a Tonal Sequence.
44. Real sequences are a fruitful source of modulation, or change of
key ; but they are very monotonous. Tonal sequences may become
monotonous if there are many reiterations.
45. When all the parts are in sequence the sequence is said to be
Harmonic. When one part is sequential and the others are free, the
sequence is termed Melodic. Ex. 82 (c) is a Real Harmonic Sequence ;
(d) is a Tonal Harmonic Sequence ; (e) is a Real Melodic Sequence.
Examples of Tonal Melodic Sequences, which are the best of all, will
be found in the two-part exercises worked out at the end of this section,
As in everything else, the more varied the sequence the more beauty
it gives to the music. Counterpoint being diatonic,* real sequences do
not enter into it. Ex. 82 (a) (c) and (e) are not contrapuntal.
Ex. 88
*
BE
3=g=ti
(c) Inclined to toe monotonous
* Diatonic music is that which is constructed entirely with th not$ of on of th
diatonic (i.e. major or minor) scales. Chromatic music includes notes foreign to t
scales, but does not cause modulation.
FIRST SPECIES IN TWO PARTS
(d) Less monotonous
17
(e) Still less monotonous
^
Compass of voices.
46. The first counterpoint exercises are written for voices. Far less
technical knowledge is required than would be needed for instrumental
writing ; moreover, the slow-moving rhythm is more suitable for
voices than for instruments.
Ex. 88 gives the compass of the voices. These are not the extreme
compasses of each voice, but the beginner should observe these limits.
If what has been said about wave-form (29, 30, 81) has been thoroughly
digested, the student is not likely to fall into the only technical fault
open to him in writing for voices, namely, that of keeping them too
long at the extreme points of their compass.
Ex.33
Soprano
Alto
. Tenor
(gve lower)
Bass
Summary and General Hints.
47. Do not write
(1) Consecutive Ists, 5ths, or 8ths either in similar or contrary
motion (18).
(2) Exposed perfect consonances, except between (a) two tonic
harmonies ; (b) tonic and dominant harmony ; (c) dominant
and tonic ; (d) tonic and sub-dominant j (e) sub-dominant and
tonic. In the case of (b) to (e) one part m< T ^S by step, the
other leaps a 8rd, 4th or 5th (88).
(8) Many perfect consonances even when they are not *cutive :
many consecutive 8rds or 6ths, three are enou$ ^'sons
in the middle of a phrase. This applies to two-p? _ ater-
point, where these intervals would sound thin d mono
tonous (8)-(18).
(4) An 8th on the leading note, or an 8th on the 8rd or th of the
scale when the implied chord is the 1st inversion o^a major
triad, except when the parts move by step in contrary
motion (28).
(5) Many repeated notes (80).
(6) Distantly related chords. Those with the least affinity are the
mediant and sub-dominant (21).
C
18
COUNTERPOINT AND HARMONY
(7) Implied 2nd inversions (18 and 19),
(8) Many consecutive chords from the same root (19 and 22).
(9) The tritone horizontally (29).
(10) Augmented and diminished intervals ; the 7th, or any interval
greater than an 8th horizontally (28).
(11) The interval of the 7th or of the 9th in two jumps (29).
(12) In jerks instead of in waves (5 and 81).
(18) Passages which hang about the same note or pitch, or keep on
returning to one note (tautophony) (80).
(14) Much Similar Motion (82 and 36).
48. Write
(1) Shapely and varied wave-forms.
(2) Varied intervals vertically which come from different roots.
(8) Sequences where possible (48).
(4) As much Contrary Motion as possible (80).
49. The Canti Fermi can be transposed for any part and any two
voices may be selected for the exercises. Those next to one another
will usually have the best effect, that is, Soprano and Alto, Alto and
Tenor, Tenor and Bass. These combinations do not lead to wide gaps
between C.F. and counterpoint.
- 50. Begin with either the tonic triad or its 1st inversion, or the
dominant triad or its 1st inversion.
51. Finish with the tonic triad preceded by one of the following ;
(1) the dominant triad ; (2) its 1st inversion.; (8) the 1st inversion of
the diminished triad on the leading note (41), which has such a strong
dominant flavour that it can be classed as dominant harmony. In some
of the C.F's. a plagal cadence will be found. In these cases the penulti
mate note of the C.F. must be the sub-dominant, sub-mediant or the
tonic, and the counterpoint must form with it either a sub-dominant
triad or its 1st inversion.
52. At a perfect, or inverted perfect cadence, the leading note has
such a strong tendency to move to the tonic that the counterpoint will
sound crude if it is not allowed to do so. This is also true wherever
domihant harmony is followed by tonic harmony, but the return of the
leading note to the tonic is sometimes delayed as in Ex, 84 at (),
Ex. 34
(a)
,.^,, M , ,,,.
58. Work the same C.F. as many times as you ean, sometimes with
the counterpoint below, sometimes above.
54. When in doubt remember that a harmonic licence matters far
less than a bad shape to the phrase. Movement precedes all else in
importance.
55. The bad inventor starts at once, to make his model, hut the
successful man first works out the idea in his brain, then makes
FIRST SPECIES IN TWO PARTS
19
of it, and finally starts on his model. This is splendid advice to the
counterpoint student. Do not write one note trusting to luck what the
next will be. Right from the start try to conceive as far ahead as you
can, then begin to write.
Example 35.
No. 1 shows what not to do. It hangs about B flat all the time and
has a succession of four Srds in similar motion.
No. 2 is better, but is tautophonous and has too much similar
motion.
No. 3 is the best ; it rises to a climax at the end.
Nos. 4, 5 and 6 are graded in the same way. No. 5 is tautopohnous,
but has more contrary motion than No. 4. No. 5 has a tiny sequence,
but No. 6 has a better one.
Ex. 35 A C.F. worked in six different ways.
1
*F-
**
-..O .
pe i
^*
**
rO 1
*&
:
r O 1
O
rn IT
Ten.
Bass
*fn
q;
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C.F.
;zr
b 5
n
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^
COUNTERPOINT AND HARMONY
A,
Example 36*
No, 1 has too much similar motion -four consecutive* CJths --but
has a good shape with the climax in the middle.
No. 2 jumps about a good deal Note the* interval of a 7th in two
skips between bars 5 and 7. The downward leaps at the end are some
what justified by the sequential fueling,
No. 8 is best ; it has a sequence and rises to a climax at the end.
No. 4 has a good deal of similar motion and the two successive'
dominant harmonies at bars 18 and 14 are weak*
No* 6 is best ; it is quite possible to add a middle part to it and to
No. 8. This may be attempted later.
Ex, 86
1
'i|('jjf' y
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*JMU,j
L*J
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afcr
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x
FIRST SPECIES IN TWO PARTS
21
s.
CLR
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Ex.87
*p L| O.F.
La
,5/ ^wo lines of JSisenack^
a German Chorale
A.
* n
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(a) An F in the lower part at this bar would make an implied 2 n & inversion
T.
B.
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Ex.88
A.
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(a) The two dominant harmonies inthis bar and the next are not so weak as
those in Ex. 36, N9 4. since there is more movement here
The sequential, effect justifies the crossing of the parts, as it gives unity
to this Example.
22
COUNTERPOINT AND HARMONY
Exercises on Section I f Major Keys,
The following C.F,*s may be transposed into any convenient key.
Those given above may also be used.
..& ft:
..,**..
""^
E5E4E=
UjgjJHZd
Minor Keys.
56. These present difficulties at first on account of (1) the number
of augmented and diminished intervals between the notes of the
harmonic minor scale ; (2) the small number of triads available in that
scale,
Ex. 40, together with the accompanying table, show the augmented
and diminished intervals, (The major scale has only one pair, the
augmented 4th between IV and VII, and the diminished 5th between
VII and IV).
FIRST SPECIES IN MINOR KEYS
23
f Aug. 4th between IV and VII.
** I Dim. 5th between VII and IV.
f Aug. 4th between VI and II.
J ' I Dim. 5th between II and VI.
f Aug. 2nd between VI and VII.
3. \ Dim. 7th between VII and VI.
[ Aug. 5th between III and VII.
4. Dim. 4th between VII and III.
It will be seen that the leading note appears in three out of the four
pairs. In fact, were it not for the melodic minor scale, the leading note
could only move to the tonic, super-tonic, or dominant.
57. The melodic minor can be used, however, the sub-mediant and
leading note being sharpened in ascending passages, and flattened in
descending. It is the ultimate direction of the altered notes that
counts. Thus Ex. 41 begins with a descent, but the ultimate direction
of the leading note is upwards. Therefore the sharpened form is used.
Ex. 42 begins with an upward leap, but both the leading note and
sub-mediant eventually descend, therefore the flattened form of these
notes is appropriate.
Ex.41
Ex.42
58. If triads are constructed on all seven notes of the harmonic
minor scale, three will be found to be dissonant. This is shown in
Ex. 43, where the minor and major triads are printed in white notes,
and the diminished and augmented in black. Out of these only those
on the tonic, dominant, sub-dominant and sub-mediant would be
available were it not for the additional triads found in the melodic
minor.
Ex.43
II
III
IV
VI
VII
Minor Diminished Augmented Minor Major Major Diminished
24 COUNTERPOINT AND HARMONY
Ex. 44 gives these additional triads and their inversions. The one
given at (a) is the first inversion of the diminished triad on the sharpened
6th of the melodic minor (17).
Ex.44
m
59. Ex, 45 gives all the intervals available above and below the
C.F,, the middle stave representing the notes of the O.F, These intervals
must not be used indiscriminately. Those marked with a cross are all
necessary for progressions where either the ascending or descending
forms of the melodic minor are used, but not for any other purpose.
If the worked-out examples which follow are carefully studied,
there need be no difficulty* It is hardly necessary to say th&t, as
counterpoint is strictly diatonic* the sharpened and flattened forms of
the leading note can never be contiguous. This applies equally to the
sub-mediant*
Ex.45
*
In Ex, 46 (1), the sequential drop of the 5th excuses the unison at
4. (54.)
Ex. 46* ThiB contains no additional Triads
1
rtr"-^
f=
C.F.
JF*=
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*
XX
^
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FIRST SPECIES IN MINOR KEYS
25
7ST"
.
r!
t=
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y
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C.F.
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11
w-*
Exs. 47 and 48 show several ways of treating the ascending form of
the melodic minor. The small black notes show the harmony.
Ex. 49, worked eight different ways, is designed to show the
numerous varieties of treatment of the descending melodic minor.
In Exs. 47 (3), 48 (2), 49 (2) (3) (4) and (8), a middle part may be
added, and in Exs. 46 (1) (2) (3) and (4), 47 (2) and (4), and 48 (1), the
same may be done if the lower part is transposed an 8th lower.
Most of the other examples can also be used if transposed to another
key. To some, such as 49 (5), an upper part may be added. The
alteration of a note here and there is quite legitimate.
Ex.47
C.R
jy ^
It, ,.,
O
.
*.
^^
-_
-e-
*
o -
-*
. j
J^H,
A.
C.R
F?
Itj r,
r
o
THi
p
V.
**
o
^v~~
S
mrv
-o-
L^j 1
LO 1
1 '
-e-
*.
LeJ
-o-
L -o '
^
26
COUNTERPOINT AND HARMONY
ft
rfr-
nr 1
^** ...-,
m
C.F.
flL
fe
-o-
fit
-Trt
Jte=
I*
JO.
^fc
=2
A.
Ex.48
1
A.
.o.r'L.
5 s
^
^
o
LJ
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TT
XT
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TT
T.
m
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o
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&
np
o
C.R
+
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O"
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o
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h ^.j
s.
T.
,-t-
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11.,:.::
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C.R
firm
p^ri
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ti ""
rt
^=
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fit
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-o.:::
^p:
g 'O
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if
mud
Ex.49
B.
FIRST SPECIES IN MINOR KEYS
27
C.F.
o
-n
-nn
O
-e
1
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,11 .
&
u nl
-rr
s.
A C.P.
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28
COUNTERPOINT AND HARMONY
Exercises on Section I, Minor Keys.
C.F's. 1 to 6 may be worked without the melodic minor. Nos. 7-9
need the additional triads given in Ex. 44.
m
linn
first two lines of Passion Choral*
ft . I "To T^TTT^-47 L I I " I " I
L. lo In \\ II"
SECTION II.
ADDING A BASS TO A SIMPLE MELODY.
60. The semibreve Canto Fermo has no rhythmic variety and only
one cadence. Its usefulness lies in the fact that it relieves the beginner
of rhythmic problems which at first might prove distracting. But
even at this early stage it is possible to begin to learn how also to deal
with the simplest tunes. The only fresh points to be encountered are
the cadences at the end of each phrase and the unequal length and
weight of the notes.
61. Cadences have already been described (41). The final cadences
should now have become familiar by use. This section introduces the
others. Being marks of punctuation they occur at the end of the
phrases or sections of phrases. But just as in speech no pause is made
at many of the commas, so the music is not necessarily held up where
the harmony is cadential. Beginners are not expected to be very
fluent : long, sweeping waves convey a deeper emotion than they are
capable of expressing. The tunes given as exercises at the end of this
section have short wave-lengths and well-marked divisions. Therefore
it is not a difficult matter to find the position of the cadences.
The all-important point to remember is that the final chord should
invariably fall on a heavier accent than the penultimate. There is nx>
feeling of having reached a point of rest, or of having reached home or
the place you are making for, if the passage leaves off in the air that
is, at a point in the bar where there is no accent.
Later, when unessential notes and discords have been learnt, it will
be found that in some cases the melody, and often some of the upper
parts, finish on an unaccented part of the bar ; but the bass which
governs the harmonic scheme still follows the rule and comes to a halt
on a heavier stress than that given to the first of the two harmonies
forming the cadence, not necessarily on the first beat of a bar. Never
theless, the majority of cadences do end on the first beat.
62. Having got well hold of the connection between the rhythm
and the cadence, the next point is one that will be easy to him who has
eyes to see and ears to hear.
Every piece of music, big or little, starts at home, fixes well in the
mind of the listener where home is and what it is like, then traverses
a course more or less exciting in proportion to the length of the journey
and the distance from home reached, and finally returns to the starting
point. This is true of the simplest hymn-tune and of Beethoven's
symphonies, of a folk-song and of Die Meister singer. It is typical of
a day's work, of a journey and of many other things in life. Etf. 50
shows a simple, commonplace little phtase which only gets far enough
30
COUNTERPOINT AND HARMONY
from home to make a half cadence at the nearest calling-point the
dominant, and then returns whence it came. Yet it is founded on the
above idea.
Ex.50
=&
3BE
63. Let us examine the cadences in $ well-known hymn-tune
St. Peter, for instance. The first section ends with a perfect cadence in
the tonic. This is a common device to fix the tonality (" home ").
Very often the second section ends in the tonic when the first does not.
In this case the second ends with a half-cadence on the dominant.
This is as far from home as we shall get. The third finishes with an
interrupted cadence and the last comes home again to the tonic.
This is one arrangement out of many. The great majority follow the
rules given below : ,
64. 1. The key must be well fixed to begin with,
2. Two cadences of the same kind should not follow one another.
This would give the impression of returning to the same
place instead of getting on with the journey*
3. The music must get away somewhere in the middle even if
it is only as far as the dominant.
4. The tonic cadence must be reserved for the beginning and
the end. Two tonic cadences in the last two phrases are
most unsatisfactory. That is why the interrupted cadence
is so often found last but one.
65. Par. 61 stated that there would be no satisfactory eadenee
unless rhythm and harmony went hand in hand. On the other hand
practically any triad will make a comma if it comes at the end of a
phrase.
66. Examine carefully Ex. 51, in which commas are made with all
the six triads as final harmonies. No. 1 consists of the first two sections
of a well-known chorale. It is written for three voices to avoid implied
harmonies. The melody is an elaborated and beautified version of
Ex. 50. Note the places where cadential harmonies produce no commas
because they come in the course of the sections and not at the end.
That marked (a) has the harmony of the perfect cadence, those
marked (b) of the inverted perfect cadence, and that marked (c) of
the interrupted cadence. The commas are made by two triads wnose
roots lie a 5th apart. In No. 2 E minor A minor, in No. 8 E minor*--
B minor, in No. 4 G C. It is natural that two triads whose roots
are at the same distance as tonic and dominant will have a similar
effect that is, a cadential effect even though they are not actually
the tonic and dominant of the key. No. 5 is given to show the bad
effect of two perfect cadences in the tonic following each other. The
tautophony in No. 6 is not mitigated by the interrupted cadence, nor
by harmonising B, A, G, differently the second time those notes
appear (30).
ADDING BASSES TO MELODIES
31
Note how the harmony of the last crotchet of the first bar of No. 5
is changed from dominant to tonic in order to prevent the unrhythmic
effect of two dominant harmonies following one another, the first on a
less accentuated part of the bar than the second.
Ex.51
First two lines of HyMn-tune, f Cassel> (1745).
IV
d*=i
> f
^
' r }
i f
r f
1 p .
^=
r '
p
1
==
<
i
t
^ i
p i
7
(J)
(Int.)
j , j
J.
JU.
32
COUNTERPOINT AND HARMONY
67. The tonic and dominant have tyrannised over music for many
years. In modern times all sorts of efforts have been made to free it.
The most successful are those which do not despise the old conventions,
but use them in a wider and broader way. The cadences in Ex. 51 are
a very small illustration of this.
68. Ex. 52 shows half-cadences on the dominant using each of the
other five triads except the tonic the usual one to precede it. Observe
the stagnant effect of Nos. 4 and 5, particularly No. 5.
Ex.52
ft 1
II -V
"T" "1
^
!
, f
IV ^
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7
J J
L *
tr
j
<o *
.r
J r f
i
1
1
r^
,r r \
L T J
rt+i
VI-
1 J , f [.=*=
V 4
J IN J J _q
rrt-^
iT
=HM
:r Ft=f
r 4 -^
n
jj ILJ ^ |
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. UJ- p m _
-r-ri
__) .
t= =
\Jr I-
' r r 'r i
r IP .r I=E
%' '
i* 5 j J J J
m-v
M J J II
1 i
*Ji| f f r r
PIT + & I'll
^. w - ' r i r
69. It was shown in Ex. 51, No. 5 that if the $ame triad is used twice
consecutively, the first time less accentuated than the second, a bad
rhythmic effect is produced. It was also shown in Ex, 52, No* 5 that
even when the two triads have two notes in common, the effect is not
strong unless there is plenty of part-movement. The following rule
covers the whole subject :
70. The stronger the accent the greater should be the harmonic change t
or the part-movement, or both.
The graduated table given below, together with Exs, 58 and 58 (a),
shows every type of harmonic change and part-movement possible at
this stage. The numbers in the table correspond to the numbers in
the examples.
71.
No.
1.
Part-movement
Vigorous. Bass moves.
Harmonic change
Triads and their first in
versions with either one
note in common or
none.
Effect
Strong.
ADDING BASSES TO MELODIES
33
No.
2.
3.
4.
5.
6.
7.
Part-movement
Vigorous. Bass moves.
Vigorous, Bass leap^ an
8th, 6th, or 3rd.
Bass remains, other
parts move.
Bass remains, other
parts move.
No movement except in
one part.
None.
Harmonic change
Triads and their first in
versions with two notes
in common.
Triads with the same
roots.
Triads with two notes in
common.
Triads with the same
root.
Triads with two notes in
common.
Triads with the same
root.
Effect
Moderate.
Fairly
strong.
Weak.
Weak.
Very
weak.
Very
weak
indeed.
Ex.53
i
i
9 (J
^tr
r^
si
1 line of
jYzeTt dan
-H
Jfc^ a^e ^o^
J r
C
\
OP
4-
9 p v
M=f
J
J
*-
8'.
~s*V *
r ' r '
W
^H=
_ij
H
i-
^-
it
^ j
it
' 8-
^i' r
- r i i
jr; gj ' Kl '
D
34 COUNTERPOINT AND HARMONY
Ex . 5 3 r , i %** * f 'w*^ 6 * <*>*&'
etc.
or (weaker)
p "1 C
ijptjl 1 ij 1 J 1 1 1 . =g
tf-t-
f==
f p tj
r f r p
f , f r
r^
r
f f"T
feN
L i-p L
r "^ i i |
etc
72. As it is the bass which governs the harmony, and as the upper
most and lowest parts are heard more easily and distinctly than the
inner parts, the movement of the bass ranks first in importance.
73. It was Stanford, one of the greatest teachers of composition,
who said that if you wish to judge the value of music you should look
at the bass. A bold, striding bass always adds strength.
74. It is just as, necessary that movement away from an accent
should be smooth as it is that there should be life and vigour in the
approach.
75. The number of harmonic changes in a bar governs the pace and
the character of the movement. Speaking generally, the quicker the
pace and the livelier the movement the fewer changes there should be.
In Ex. 54, (a) to (e) are arranged -in order, the quickest and liveliest first.
ADDING BASSES TO MELODIES
35
In Ex. 54 (b) the harmonic changes are so slight that the rhythmic
pattern, | J J | J J J is still felt. The pattern of Ex. 54 (c) has the
effect of tying together the second and third beats of the bars. This
makes the weak end of the bar heavier just as (a) makes it lighter.
The three changes in each bar of (d) suggest a slower pace and more
sedate character. Ex. 54 (e) has a different number of harmonic
changes in each bar. It breaks the rule given in (TO), has no pattern,
and is disorderly and ineffective.
In Ex. 54 only the harmony explained up to this point is used.
The passing notes and discords which come later on will make it much
easier to get perfect unity between rhythm and phrasing, harmonic
change and part-movement.
Ex.54
76. As it has been found necessary to move the parts and alter the
harmony where repeated notes occur in the melody, so it will be found
just as important to give two or more chords to the longer notes. Ex. 55
would be very slow and dull if all the parts moved in notes the same
length as those of the melody.
77. This kind of movement should be done in a way which leads on
naturally to what follows. The first and fourth bars of Ex. 55 would
sound very crude if written as at (a), for this is movement for the sake
of movement round one spot, not movement to a definite place first
conceived.
36 COUNTERPOINT AND HARMONY
Ex. 55
78. Generally speaking the more movement the better, for movement
means energy and the lack of it stagnation, It should be fairly regular ;
a few isolated notes at a much slower or quicker pace than the rest
sound jerky and meaningless.
79. It is quite simple to tie mentally repeated notes and to reiterate
long ones, so that the second, section of Exercise 2 given at the end of
this section would be heard as in Ex. 56, and the first section of No, 5 as
in Ex.57. Weak musicians get their rhythm from the music as they
perform it. This may be called passive rhythm. The rhythm flows from
the strong musician into the music. His is active rhythm. The weak
performer's time always goes wrong where long notes or rests occur,
for here the music ceases to force each beat upon the mind. The strong
performer feels each semibreve like this
J J J J . One finds a similar tendency in students of harmony
and counterpoint. Those who are energetic instinctively feel the
beginning of Exercise 5 as in Ex, 58. It is this sense of beat which
prompts them to move their parts and their harmonies.
Ex.56
fel
'i 1 ' i
Ex. 57
Ex.58
ADDING BASSES TO MELODIES
Ex.59
37
'C&ssel'
In this example all the minims have two chords from different
roots or two positions of the same chord. This is not absolutely
necessa^ but it has been written in this way to show that it is possible
Notice how any sequential feeling improves the bass, and how differently
Xsttwo sections are harmonled from the first two There are many
more ways of doing this tune, and the student should work Exs. 59 to
62 himself more than once.
Ex.60
H. Lures (1596-1662)
38
Ex.61
COUNTERPOINT AND HARMONY
n
~~
I...
^=^
r u i
r^
J
-
<!
;,'n B : ":..'.'
_ ^
5f
t=
JL ^
:- 1 -:^- 1 "--..-, .
J ,
^L\
*
9 '
^
Hh
^r~
-^
fcziq
,.^i-
r 1~ ;
;;T^::^J
i^ v ~xSj
*
= **1
: Ff(5=
P r
r9 "
*=
~p
^
!_^
i p
#
=='
I -
=NS=
-=F=
3Bn =^=
g "
!
Z?3
=sb3
3^ '
fZ (* - 1
rfi
|-^
-= ===
*
^-J::;,.^
n
5
jL .j
M
fcr~
11
1=
^ Hi
The small black notes show the harmonies (56 and 57). Notice
how the sub-sections of two bars are not allowed to have marked
cadences, these being reserved for the sections of four bars. This makes
the tune flow along without too many stops (65).
80. Tunes in triple time present more difficulties at first than those
in duple or quadruple time, because two unaccented beats follow each
accent' The following table, taken in conjunction with Exs. 62-64,
gives every possible combination of part-movement and harmonic
Examples
in
62, 68 and 64.
(a)
(d)
change in triple time.
No.
Part-
movement
Harmonic
Changes
m
1.
2.
3.
Every beat.
Every beat.
1st and 3rd.
Every beat.
1st and 3rd.
1st and 3rd.
Good.
Good.
Good.
4.
Every beat.
1st beat only.
Good.
ADDING BASSES TO MELODIES
39
Effect Camples
jj m
A heavier stress on 54 (c)
the second beat.
It is sometimes
useful, but be sure
the tune demands
it.
The same as the
preceding but not
so marked.
Better avoided for
the present.
Better avoided.
N.B. Leaps of a major 6th are permissible outside strict and XVIth
century counterpoint, also leaps of a diminished 4th or 5th,
provided that the part making them returns immediately to
some note within those intervals.
No.
5.
Part-
movement
1st and 2nd.
Harmonic
changes
1st and 2nd.
6.
Every beat.
1st and 2nd.
7.
2nd and 3rd.
2nd and 3rd.
8.
Every beat.
2nd and 3rd.
Ex. 63
(4)
(a)
U)
J IJ J
^
(c)
(5)
(a)
(b)
^
(a)
|J-L J J J i
(a)
|| II
')
1 i
r^j
i r i j i
r)
^^-^
r J J
-^i i i i
J "1-\
III
>=J=J=
H 1 1
-i f 5
J-J--H
J J
E^=^
r f J
^ J J J
J J
J ! J.-
u r r i
r r ^
(b)
jf L j
v*/
1 J " j 1
irTTl
H f- 1
n ^^
**i r \~
H
I J r
Tl * BJ
-f 3 f
f J'
L f I
> J r
ir r r i
J ! 1 J
T r j i
When the interval of the 5th between bass and melody is suc
ceeded by that of the 6th, one of the two parts remains stationary, as in
40
COUNTERPOINT AND HARMONY
Ex, 62, bars 5, 9, 10, 12, 14, 17, 18, 19 and 20, the harmonic change is
so slight that it is hardly noticeable. The second note in the moving
part then partakes more of the character of a passing note (104),
Ex.63
Melody by Dowland (1583-1826)
Hn
rff
p
H i
I, J j i
j
' r
(a)
r r r
()
' j r
j j i
r J J
-
*-
M
r i ' i
=~ J
_j ^ j
-j H
r r r i
(a)
Ex.64
Melody by H.Purcell (1658-1695)
W'-t
(C)
'<0
<aj
Exercises on Section II.
Tunes to which basses are to be added
r r r
r r
J J i
u j r
ij. j j
riffrrirrrj i jt
ADDING BASSES TO MELODIES
41
irrr j 'rrr '
f
rrNirrr ir
J. I J J
nr nrr rnfrMi J J
*
J J
From AndernacJi Gesangluch (1602)
l^JJj
11 I J JiJj
1^ j |j j J J;
From La, Weillee (1782)
=3=3=1
J j j u J J |
Melody by Melchior Vulpius (1560-1615)
^
r r r r i- r
in
L. Bourgeois (1540)
U J J J I ..^
v r r 1
"
r
TO
I 1 1 i
rl
t=t=
ty* "
U J J J i
L_^ L
1 Ul
L^
i
~0 n \
L. Bourgeois
10
o *
_ I I U J J p
ty o J J |g g rj [
42
COUNTERPOINT AND HARMONY
Jpl I
ft) O gl
if
Minor Keys
ufrtJ Ij J J f [If f J H r l f J
J J J M J J J IJ J J J
33C
Ouseley (1825-1889)
13
JtssUf meii
irrrn-
German Chorale
German Chorale
/Tv
ADDING BASSES TO MELODIES
Major Keys
Triple Time
dulcz jubilo(XIV
IM i
i j \fi j
17
fir Mr nr M J J 'r rir f lj
i=
German, Traditional Melody
18:
r Mr JJJ U
ii
German Traditional Melody
r
Jij. ju JJ
English Traditional Melody
Copyright
%/ V ^ I | - - ^ ^
Dowiand
foJ J u j ij J u nJ r'r J |J J
21
Ju j ij JiJ tieJ r
J n
r 'r r r nr
Ju jij J
COUNTERPOINT AND HARMONY
_ front Pi at C&ntionts (1582)
22:
-tf
4^E
s- 2
-*
^
;: ;",:
b^
Minor Keys
(C minor)
V I i p "F
^
m frirr j i^ J
Ji,
ir rM r
25:
ir r
G.Berg (1775)
O ttrj hO-
SECTION III.
MODULATION.
81. Modulation, or change of key, can now be learnt in its simplest
form; that is, from the tonic to the dominant, subdominant, and
relative minor or major. The object in referring to this subject so
early is that a knowledge of modulation will enable the student to
harmonize a much wider range of melodies. Modulation is not difficult ;
it is too easy. Therefore, the student should endeavour to make his
music interesting with as few modulations as possible. Change of key
gives variety, but too much of it causes restlessness and incoherence.
It should be proportionate to the intensity and excitement of the
music. That is why most of it occurs in the middle of a composition,
as, for instance, in the development section of sonata form. The
earliest exercises in harmony and counterpoint cannot express deep
feeling (31). Therefore many modulations, or modulations to remote
keys, would be unsuitable to them.
82. Modulation is effected by the introduction into any part or parts
of the sound or sounds wherein the new key differs from the original
one.* Modulation is also strongly influenced by cadences. The related
chords which form the perfect and plagal cadences are so much associated
with the keys to which they belong that, when used to conclude a
phrase even when that phrase has begun in another key they give
the effect of a modulation. In Ex. 65 the fore-phrase begins and ends
in C. The after-phrase, without any appearance of B|?, the only sound
not common to both keys, finishes with a perfect cadence in F. This
gives the effect of a modulation to that key. If a Bfc) were introduced
into the after-phrase it would hold back the music in the key of C.
Ex.65
rfi
MnH
1f~l
N=|
A
t?=
M^
;
ij j J 71
d
?
In Ex. 66 the after-phrase ends with a plagal cadence in the key of G,
no F# having been used. This has the effect of a modulation to the
key of G. Any appearance of Ftf in the' after-phrase would suggest the
key of C so strongly that it would create the feeling of .a half-cadence,
on the dominant of C, not a modulation to G.
Ex.ee
-
Jj4 J
*Note the exception to this in (84) .
46
COUNTERPOINT AND HARMONY
Ex. 67 is a modulation to A minor made in a similar way. Although
Gt| appears in the after-phrase it is preceded and followed by two triads
which strongly suggest A minor.
Ex.67
3035
n. ...' r
*J J
Exs. 68-70 are given to show that modulation may be made by the
introduction of the sound, or sounds peculiar to the new key without
cadential harmony. Naturally, as cadences end phrases, this kind of
modulation only occurs during the course of a phrase which goes back
at the end to the old key, or goes on to a third key. This is called
Transitory Modulation.
Ex.68
afe
" f
L-T
i^i
Ex.69
Ex.70
83. The type of modulation treated of at the moment is that which
includes both factors, cadences and accidentals. In Exs. 65-67 it is
difficult to avoid accidentals ; in Exs. 68-70 it is inconvenient to avoid
cadential harmony. These examples are given to show the influence
of each of the two factors separately, When both are used, as in
Exs. 71-73, the sense of the new key is much stronger.
MODULATION
47
Ex.71
Ex.73
84. When the note peculiar to the new key is at once contradicted
and the chord containing it is followed immediately by some chord
strongly suggesting the old key, there is no modulation. The passage
is then said to be Chromatic. Simple instances of chromatic harmony
are given in Exs. 74-76. No such progressions must be written until
section XVIII of this book is reached, which deals with that subject.
Modulations should be made as early in the phrase as possible. If the
change is delayed too long the effect is apt to be jerky. Having
determined to proceed to a new key, get there by the shortest route
without looking back.
Ex.74
Ex.75
Ex.76
48
COUNTERPOINT AND HARMONY
85, False Relations are said to occur when an accidental introduced
into one part is contradicted in another part in the next chord (Exs.
77-80). Their effect varies. They may sound contradictory and
illogical when both of the chords containing the false relation come from
the same root, the 3rd of the chord varying from major to minor,
as in Ex. 77. But when the chords come from different roots, as in
Ex. 78, the effect is often harmless. The false relation caused by the
juxtaposition of the sharpened and flattened forms of the leading note
of the minor scale has no bad effect (Ex. 79). Later on it will be found
that both forms of this note can be heard simultaneously without bad
effect, as in Ex. 80. No definite rules can be given, but where there is
ugliness there will be some reason for it ; some hesitation between one
key and another, or aimlessness in the part-writing.
Ex.77
Ex.78
Ex.79
Ex.80
m
f
S
86. Modulation from a minor key to its relative major, or from a
minor to its dominant or subdominant cannot, of course, be effected
by cadence alone. Notes foreign to one or other of the keys would
appear whether a perfect or a plagal cadence in the new key was
employed. Modulation from a minor to its relative major by means
of notes peculiar to the new key and by cadence is very simple and
needs no comment (Ex. '81).
Modulation from a minor key to its dominant or subdominant is
rather more involved than from a major. In major keys the dominant
triad becomes the tonic triad of the new key. But the dominant triad
of a minor key is a major triad, and the tonic triad of the new key is
minor. Moreover, when going from a major key to its dominant or
subdominant, four triads will be found common to both, and three
when proceeding from major to relative minor or minor to relative
major. But when modulating from a minor to its dominant or sub-
dominant, unless the additional triads mentioned in (58) are used,
there is only one triad common to both keys, namely the tonic triad
when modulating to the dominant, and the subdominant triad when
modulating to the subdominant key. When the additional triads are
used, many more links are provided. This is made clear in Ex. 82.
Ex.81
MODULATION
49
Dominant
(G minor)
Tonic
(C minor)
Sub.Dom.
(F minor)
Ex.83
Diatonic triads in white, additional triads in black notes. Roman
figures refer to the 1 degrees of the scales.
IV V
1 aL I" *n 1
- it--
Lp 1]
%T :
VI '^
VII a)
U -
j a) ,
III ') i
Q L k t -4.
--p. u p.
IV ^
>g i>8 i,ft=
5 3
(aO i
TO g ">
2.1 .
D.
T.
S.D,
The smoothest and easiest modulations are those in which some
chord common to both keys is approached from the old one and quitted
in the new, and acts as a link between the two. Ex. 83 shows a modula
tion from C minor to its dominant, made with the help of the additional
triads, in eight different ways. Ex. 84 shows a modulation from C minor
to its subdominant in nine different ways.
87. Modulation may be compared to travelling. Cadences in the
keys whereto the change is made are like stops in the course of a
journey (62 et seq.). A hymn-tune or chant with one modulation to
the dominant resembles a short journey to a neighbouring town and
back, whilst the development section of a symphony suggests an
exciting and adventurous trip through many lands. Music with too
frequent modulations and a full-stop at the end of each is as irritating
as a long journey in a stopping train. Music with many modulations
and never a cadence would be as tiring as travelling all day without
a stop.
\ E
50
COUNTERPOINT AND HARMONY
Ex 88
The letters in brackets indicate wkioh additional triads from Ex. 82
are used. , ...__
1
-r r r
r r
\nt
^
m
MODULATION
51
Ex.84
When working the Canti Fermi do not allow the notes wherein the
. -r
No. "to 6 to D ; No. 8, tar 6 to B r No. 10, to 15 to D.
52 COUNTERPOINT AND HARMONY
Exercises on Section HI.
C,F.'s which modulate. In those with odd numbers the modulations
are clearly indicated by the accidentals. In those with even numbers
the modulations are suggested only. The student should work each
one in several ways and with different pairs of voices, transposing to
suit the compasses of the voices chosen.
^ To the Dominant
--,-.. _.
_.
1 A_ ! e u 2 u_
A To the Dominant
jfr* ' O ~"
rr - 1 -
^ : .*>.."' ' ""
~~r 1
^ To the Sub -dominant
* o
u
u
*- ~l <5 -
*/ ^^
^ To the Sub-dominant
^_ M_ _
H
* To the relative minor
.. H
5 A) V | * | | ** | **
A To the relative minor
U
. 1
c < o i .. I,- i ir
A { To the relative major
1
- To the relative major
1 Q 1 11 I 4
^*~\ it [.
-rHI
^ ! To the Dominant
"o r ; -
rhvs ""
- B
9 {fa fr !<* , ...
To the D omina n t
-^ 1}U ^
. t' '
A ( To the Sub -dominant
3 ' ^ J ^jr- 4 -
O ^ ' " ty> "
____
*
*> , ^ t^y ^
A To the Sub-dominant
Li 1 (jo 1 11 .1
1 " -o-rir
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zrmrriizr
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MODULATION 53
Modulating melodies to which basses are to be added.
Hymn. Tune (im)sligMy altered
Jesu f meiite Zuversicht. J. Criiger (J598-1662)
Welsh Symn Melody
j ' ' j
Songl. 0. Gibbons (1583-1625)
.u.1,1 uj.. i- .1.1
jj
j j
pe
n
-
COUNTERPOINT AND HARMONY
LiebsUr Immanuel (1679) .slightly altered
m
II I J II
O 1
3^4
SECTION IV.
ADDING A MELODY TO A GIVEN BASS,
88. Hitherto, except in the case of the semibreve Canto Fermo, the
student has only had to write a bass to a melody. It is now time that
he wrote melodies for himself, firstly above a given bass, and afterwards
writing both melody and bass himself. To do this he must know the
essentials of a good tune. These all emanate from inspiration, or
enthusiasm; that is, the stimulation and incentive aroused by the
intense love of the work in hand* This stimulation always shows itself
in movement of some kind, just as the lack of it takes the form of
stagnation. In music the movement is shown by a vital energy in the
rhythm. This is the first essential. The other two are beauty of
phrase-shape, and perfect balance of phrases*
89. (I) Rhythm. Until passing notes and suspensions have been
learnt the student is restricted as to variety of rhythm. But it has
been shown in (75)-(79) and by Exs. 59-64 that even at this early stage
considerable variety can be achieved.
There are three ways of giving stress to a sound : (1) to place it on
a strong beat of the bar ; (2) to make it of longer duration than its
neighbours ; and (3) to approach it by leap, especially an upward leap.
Bars are of arbitrary length, and if most of the long sounds occur on
strong beats and are approached by leap, the resultant tune will incline
to monotony and a sing-song lilt The immutable bar rhythm should
be a sort of background upon which the composer weaves his tune by
the help of the other two factors length and leapand by phrase-shape
and balance, much as the lead in the old stained glass windows acted
as a background and was yet made to help in the decorative effect.
The repetition of a rhythmic pattern in the course of a tune unifies it.
But if the intervals repeat, and especially if they repeat at the same
pitch, then a considerable time must elapse before the repetition, so
that it comes back with freshness. Even under these circumstances it
is better not to repeat the whole section, but only a part of it, allowing
it to finish in some new and more interesting way. Repetitions of
rhythms but not of intervals, or repetitions of rhythms and intervals,
but at a new pitch, always help, and no space is needed between such
repetitions, as they differ enough in themselves. Subtle changes in
intervals or in pitch on repetition can be of enormous assistance.
Examples of repetition well used from the given melodies at the end of
Section II, are as follows :
No. 4, bars 9 to end. The order reversed on repetition.
No. 5, bars 5-10, Rhythm the same, but intervals and pitch
altered.
No. 11, bars 4 to end* Rhythm and pitch the same, intervals
altered.
5C COUNTERPOINT AND HARMONY
90. (II) Phrase Shape. Much has already been said on this subject
in 29-31, and very little need be added, A leaping, vigorous bass gives
life to the music, but movement by leap and by step is more evenly
balanced in a melody. There is much more movement by leap in a
good bass than there is in a good melody.
91. (Ill) Balance, This is the art of constructing phrases and their
integral parts so that the tune has a satisfactory architectural form,
one part balancing another. This is not a book on form and this part
of the subject cannot be treated of here more fully than will help the
student to write in the simplest forms.
Phrases usually consist of two sections, the fore-phrase and the
after-phrase. The second is a response or answer to the first. There is
a cadence of some sort to mark the division between them. An eight-bar
tune with fore-phrase and after-phrase of four bars is a phrase of this
kind. Examples of it are given in the melodies at the end of Section II,
Nos. 1, 11, 12, 13, 19 and 20. Four simple forms in which the student
can write are given below :
(1) The eight-bar tune mentioned above which is the simplest of all.
(2) A ten-bar tune made up of :-~
Fore-phrase of 4 bars : cadence.
After-phrase of 4 bars : cadence.
Coda of two bars : cadence.
If before the coda there is a perfect cadence in the tonic, the
final cadence should be plagal, or vice versa. But it is not
absolutely necessary that the after-phrase should end with
a perfect cadence, vide Melody No. 8, Section II.
(3) A twelve-bar tune with three sections of four bars, the last
being a repetition, more or less, of the first, the second being
a contrast. The cadence at the end of the second section
should be in the dominant or relative minor, so that the
tonic key comes freshly at the repeat. When other modula
tions than those to the attendant keys have been learnt,
this and similar cadences can be considerably varied.
Examples are Ex. 59, and Melodies Nos, 4 and 5 in Section II.
(4) A sixteen-bar tune of two phrases of eight bars, each with a
fore-phrase and after-phrase of four bars. This is perhaps
the commonest of all forms and can be found in all kinds
of music from Beethoven to a Barn Dance. Interest can
be imparted to it by variety in the other two factors-
Rhythm and Shape and by modulation and well-ordered
repetition. Examples are Exs. 61 and 85 and Melodies
Nos. 18, 23 and 24 in Section II.
An analysis of folk songs and the themes of the great masters will
show how many other plans there are on which to build a melody,
and how many melodies there are founded on the four simple forms
given above, but varying in some charming way from their somewhat
stiff and conventional outline.
92. There are many good tunes which have no variety of rhythm
and yet which carry one along with them. Many of these, like the
ADDING MELODIES TO BASSES
57
German Chorales, have superlative beauty of shape and balance.
On the other hand examples of infectious, attractive rhythm can be
found where the form is commonplace and the compass so restricted
as to prohibit any very great beauty of shape. It has already been
said that multitudes of good tunes have been written in commonplace
forms, particularly the fourth form mentioned above, in which the
vitality of rhythm, or beauty of shape, or both, are so great as to make
one overlook the conventional form.
93. Ex. 85 is a very poor tune. Touch it up as you may it can
never 'be anything but commonplace. But it is given in order that the
student may feel the improvement gained by imparting to it the various
essentials mentioned in this section. At (a) it has more variety and
point in the rhythm than at its first appearance. At (b) the phrases
are given a more interesting shape by altering the exact repetition of
the last phrase and of the sequences at bars 2 and 3, and 9 and 10,
and also by eliminating one of three awkward stops (bar 12). At (c)
the fore-phrase is shortened to three bars. It still balances with the
last one because the final note is reached at the penultimate bar, and
this gives the last phrase the effect of three bars.
Ex.85
58
COUNTERPOINT AND HARMONY
94. The first three basses given are those of well-known tunes,
harmonized with triads and their first inversions only. In working the
others, make free use of the triad going to a first inversion, or the
reverse, whilst the bass remains stationary, i^., 5-6*, or 6-5
(Ex. 86 (a) and (&)). Also use the stationary note in the melody whilst
the bass moves from a 5th to a Oth, or vice verm (Ex. 87 (a) and (6)).
This will help to avoid the feebleness and tamencss that result if the
melody merely imitates the rhythm of the bass,
Ex.86 (the Bass from N9 7)
5665
Ex. 87 (the Bass from N?7)
iL
r
5 6
Exercises on Section IV.
6 5
Wsll-known, Hymn Tune
for)nl
Well-known Old
Melody
' The figuring of basses is explained in (103) .
ADDING MELODIES TO BASSES
59
Andante
Form If
60 COUNTERPOINT AND HARMONY
Minuet
Solemn March
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SECTION V.
THREE-PART WORK IN THE FIRST SPECIES.
95. The whole of the work done in Sections I to IV can now be
re- written in three parts. The use of the C clefs for Alto and Tenor is
strongly recommended. Without a knowledge of these clefs it is
impossible to read an orchestral score, and facility in the use of them is
demanded at all examinations for university degrees and reputable
diplomas.
96. Very little fresh knowledge is required for writing in three
parts ; it may be divided into three heads : (1) Position of Chords ;
(2) Doubling ; (3) New vertical intervals between the two upper parts.
97. (I) Position of Chords. Until four or more parts are used it is
sometimes difficult to avoid gaps of over an octave between two of
them. This often happens when writing for Soprano, Alto and Bass,
or for Soprano, Tenor and Bass. In the first case there will be a
greater distance between Alto and Bass than between Soprano and
Alto, and in the second a bigger gap between Soprano and Tenor than
between Tenor and Bass by reason of the compass of the voices. These
gaps cannot always be avoided, but the following general principles
should be adhered to as far as possible :
Do not allow a gap of over an octave between any two parts unless
(1) the gap lies between the Bass and the next part above it; (2) a far
more interesting part progression is obtained by means of it. If a
gap is made, it should extend for as short a distance as possible.
The reasons why gaps sound better between the bass and the next
part above than between the others are twofold. (1) Low sounds give
more harmonics than high ones, and therefore a gap above the bass is
more or less filled by the harmonics of that part (23).
sounds better than
sounds better
than either. (2) In the case of voices, scarcely any tenors and not
many sopranos can get any carrying power from their lower notes.
For this reason voices nearly always sound well in soft passages, even
when some are at a very low and others at a very high^ part of their
compass. But the louder the music the more essential it becomes to
keep each voice at a pitch at which it is easy for it to emit a full sound.
COUNTERPOINT AND HARMONY
Basses and contraltos can usually do this down to the low B flat, but
tenors are not much good below F, and sopranos begin to fall off between
this note and the low C. This of course only applies to the chorus ;
picked solo voices are different. Such a chord as this
would never sound well for chorus ; the tenors would be too prominent
and the basses would scarcely be heard. Chords are said to be in close
position when each part sounds that note of the chord next above the
part below and next below the part above.
They are
m open position when an unsounded note (or notes) of the chord lies
between each part.
Chords sound richer and fuller when
the parts are nearly equidistant from each other.
98. (2) Doubling. The root of a triad is the strongest note to double,
after that the 5th and minor 8rd, and last and weakest, the major 3rd
(16, 23 and 24). The worst places for a weak double arc at a stress (89)
that is, at a strong beat, a note longer than its neighbours, or one to
which a leap, especially an upward leap, has been taken. The converse
is also naturally true, that the most inoffensive places for a weak
double are on a weak part of the bar, on a short sound, or at a place
where the parts making the double do not leap, but move by step.
The outside parts are heard more than the inside ones, and it is the bass
which determines the chord (15 and 18). Therefore, in first inversions
of major triads, where the bass has the major Std, a doubled major Orel
is more prominent than when the bass has the root,
99. The beginner makes more mistakes over consecutive perfect
concords and doubling the wrong note of the chord than over anything
else. A sharp lookout should therefore be kept for consecutivcs, remem
bering that although in two parts there is only one chance of them, in
three they may occur between (1) the highest and the middle part ;
(2) the highest and the lowest part ; or (8) the middle and the lowest
part. Consecutives are taboo, but weak doubling is unnoticeable when
the movement of the parts is of the right kind (86),
100. Incomplete triads sound best, generally speaking, when the
3rd is present. But there are numerous occasions when a triad consisting
of a doubled root and a 5th is quite acceptable, as for instance, where
an austere, or bare effect is wanted (Cp, the second quaver in basses
to which melodies must be added, No. 9, Section IV) or where the chord
FIRST SPECIES IN THREE PARTS
is so short and unimportant rhythmically that its composition is not
noticed (Ex. 88). There are many cases where, at a cadence, all
three parts will finish on the tonic and its octave. This will almost
invariably be the case where a melody makes a cadence by a fall from
the super-tonic to the tonic, and the penultimate chord is the dominant
triad, for the middle part will be on the leading-note, which must
proceed, along with the other two, to the tonic. The exception would
be where there is no 3rd in the dominant triad (Ex. 89), but this would
be bare and hard as a rule.
Ex.88
m
tr
r
r
Ex.89
usual
unusual
101. (3) New Vertical Intervals between the two upper parts.
A.S all three notes of the triads will now be sounding simultaneously
(except when one of them is doubled) three new vertical intervals will
appear between the upper parts, namely the perfect and augmented 4th
and the diminished 5th. No new intervals occur between any part and
the bass, and the relationship of each of the upper parts to the bass is
governed by the rules of two-part counterpoint already given. It is
only the relationship of the two upper parts, one with the other, that
is new. Consecutive perfect 4ths may occur freely between these, but,
like other intervals, a great number will lead to monotony. The other
two intervals, , the augmented 4th and the diminished 5th, are slight
dissonances.
102. These intervals are only found in one chord of the student's
vocabulary up to this point, namely, the first inversion of the diminished
triad (17). This chord occurs on the super-tonic of major and minor
scales, on the subdominant of the minor scales, and, as an additional
triad, on the tonic of the minor scales (Ex. 90). The two notes of the
augmented 4th which form the dissonance have a very slight tendency
to progress to two others by way of resolution : the 6th from the bass
to rise one step, and the 3rd from the bass to fall one step (Ex. 91).
This is felt in a stronger degree when the first inversion on the super-
tonic is followed immediately by either the tonic or submediant
triads (Ex. 92). When followed by any other triad or its inversion the
tendency remains, but in a less marked degree. In such cases one or
both of these notes may leap without bad effect.
64
COUNTERPOINT AND HARMONY
(1) The leading note may leap upwards except at a cadence when
it is the highest part. Then it should go by step to the tonic.
(2) Either note may leap, provided it returns in a short time to
the note of resolution (Ex, 93).
(3) When followed by a chord having two notes in common with
it, the progression is already so smooth that a leap of cither
or both sounds is not noticeable (Ex. 94).
(4) Movement by step in either direction is always good, and
effects any slight resolution that may be required (Ex. 95).
In strict counterpoint the diminished 5th may be preceded,
but not followed, by a perfect 5th (Ex. 96). The student
would do well to abide by this rule even when not writing
strict counterpoint until four-part writing is reached.
Consecutive augmented 4ths and diminished 5ths are
harmless (Ex. 97),
(5) The subdominant, in common with all dissonant notes, may be
resolved by remaining to be a part of the next chord
(Ex. 98).
Ex.90
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Ex.91
Ex.93
Ex.93
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Ex.95
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FIRST SPECIES IN THREE PARTS
65
Ex.96
Right
avoid
Ex. 97
Ex.98 '
It follows from all this that the element of dissonance is very slight
and that there are few cases where an arbitrary progression is necessary,
or where, if such cases arise, the average ear will not subconsciously
suggest the right movement of the parts.
A few preliminary exercises are given below in which the student
is required to add one part, two being already given. Before writing
these, middle parts may be added to Ex 36, 3 56; Ex. 46 4,
Ex. 47, 3 ; Ex. 48, 2, 4 ; Ex. 49, 2, 3, 4, 8 ; Exs. 61, 62 and 63 \\he
these and the preliminary exercises below have been completed all
the Canti Fermi, Melodies and Basses m Sections I to , IV sho Id be
worked in three parts, selecting various combinations of the fom xoiees.
103 It will now be necessary for the student to learn the figuring
of basses. This is a kind of shorthand to indicate the chord above any
bass note. The figures show the intervals above the bass made by the
notes in the chords. An accidental before any figure indicates that a
5j^ddrtal must be placed before the note to which the
figure refers Accidentals alone, without a figure ^wa rrfertojfce
3rd above any bass note. Thus, at (a) in Exercise 2 the Alto must smg
C sharp, a 3rd above A, the bass note. Triads are not figured except fm
a specfal reason, usually when an incomplete triad is required > Thu
at (b) in No 2 only the 8th and 5th are required. A first inveision is
SdicaJed by the figure 6. The following signs-6-5, or, 5-6, mdicate
that the 6th of a first inversion falls to a 5th, whilst the 3rd remains,
or vice versa.
06
COUNTERPOINT AND HARMONY
Exercises on Section V.
Add a Tenor
'Gott d#s Him>n&l$! Gorman Chorale
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42
FIRST SPECIES IN THREE PARTS
67
Add an Alto
A us der Tiefe. German Chorale
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68 COUNTERPOINT AND HARMONY
5 AJJ 4 4. AI+ Meludy adapted from $(ntrg<tois ly J S.Bach
" Add a 1st Alto _^ -*
6. Add a ^nd Tenor. This tune is inthe-ffiolianMode, Use no C sharps. The consec
utive 5ttf 8 are between one phrase and the next, and by contrary motion
SECTION VI.
TWO NOTES AGAINST ONE.
THE SECOND SPECIES OF COUNTERPOINT.
104. This is the commencement of ornamentation. Having learnt
the rudiments of the constructional element of counterpoint and
harmony, the student can begin to beautify and decorate his work.
He has erected plain columns ; he can now proceed to carve the capitals,
but in quite elementary style. Henceforward every note he writes
will be either a harmony note, that is, a note found 'in the particular
chord established at the moment, or an ornamental note which will not
be a member of the chord. The ornamental notes used in 2nd species
are divided into two classes : (1) the Slow Mordent and its inversion,
(2) the Passing Note. The simpler ornaments in music, the Mordent and
the Turn, Ex. 99 (a) and (c) with their inversions (Ex. 99 (b) and (d) )
and the various forms of Appoggiatura, single (Ex. 100 (a) ) and
double (Ex. 100 (b) ) are all formed from the two notes lying next
above and next below a harmony note. Strict counterpoint does not
include the appoggiatura, as does harmony, for it only treats of prepared
and passing discords. But it has a slow prototype of both the mordent
in the 2nd and 3rd species, and the turn in the 3rd species (four notes
against one) (Ex. 101).
Ex.99
(a) (b)
Ex.100
(d)
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70 COUNTERPOINT AND HARMONY
105. The first note in the bar in 2nd species must always be a
harmony note, and must follow the rules of 1st species given in Section I.
The second note in the bar may be one of the four following : (1) a
Harmony Note of the same chord as is established on the first note ;
(2) a Harmony Note with the C.F., but not a memjber of the chord
established on the first note ; (3) the note next above or below a first
beat harmony note which returns immediately to that note (Ex. 101,
(a) and (&)) ; (4) a Passing Note.
(I) Harmony Notes belonging to the first chord in the bar.
Any part in 2nd specier may leap to either of the other two notes
of the triad established on the first beat, or leap an octave, provided
that it conforms to the rules of horizontal part-progression given in
(27-39).
(2) Harmony Notes with the G.F. not belonging to the chord
established on the first beat.
The use of these notes will cause a change of chord at the second
minim, in other words, two chords in a bar. Although this is permissible,
it is not advisable to begin with. The study of strict counterpoint like
all good education, eliminates some difficulties for a time in order to
concentrate the mind on others. One of the chief difficulties of the
beginner is to find the right rhythmic points for chord changes. This
difficulty is eliminated from strict counterpoint by the rule that there
shall be one chord in a bar. If this rule is relaxed, and two chords are
allowed, it really augments the student's difficulties by increasing the
number of problems to be solved, but it does not of necessity make bad
counterpoint. Naturally, if a change is to be made at a weak part of
the rhythm, a smooth change will sound best, that is to a triad having
two notes in common with the one first established, or one in strong
relationship to it (Ex. 112, bars 8 and 17). Therefore, in writing in
two parts, a mental note should always be made of what chord is
intended on the first minim. The only reason for making two chords
in a bar should be to obtain better part-writing, not to get out of a
difficulty.
(3) The " Slow Mordent. "
Any harmony note may proceed to the next note above or below it
and then return, so long as it does not make (1) Tautophony (Ex 102)
(2) Consecutives (Ex. 103); (3) a 7th moving by similar motion to
an 8th (Ex. 104).
Tautophony is avoided when "slow mordents" occur at the
summits and troughs of the waves (Ex. 105). A number of them in
sequence i$ excused by the symmetry of the whole phrase even if thev
do cause repetitions (Ex. 106).
Ex.102 f t Ex.103
SECOND SPECIES
71
Ex.104
Ex.105
Ex.106
(4) The Passing Note.
Passing notes are the steps between one harmony note and the next.
They should be included. as often as possible, and used more frequently
than any of the other three classes, for they move along and get some
where, whereas even the " slow mordent " only marks time (Ex. 107).
Instead of returning, as does the " slow mordent," they move on by
steps of a 2nd in the same direction until they reach the next harmony
note (Ex. 108). With them also, tautophony, consecutives and 7ths
going to 8ths in similar motions must be avoided ; as well as 2nds
proceeding to unisons (Ex. 109) unless the parts cross and the moving
part proceeds right through the unison (Ex. 110). Seconds proceeding
to thirds in similar motion do not sound very smooth, especially minor
seconds, since like the foregoing, there is a slight dissonance (the 2nd
on the weak minim) that is never resolved (Ex. 111). However, very
little clash is heard (Ex. 132, 1, bar 3).
Ex.107
M
Ex.108
Ex.109
Ex.110
Ex.111
72 COUNTERPOINT AND HARMONY
106. Example 112 has the second minim in each bar numbered
according to which of the four classes enumerated above it belongs.
It will be noticed that, out of 28 bars, there are 13 cases of passing
notes, 8 harmony notes belonging to the first chord in the bar, 2 cases of
two chords in a bar, and 1 " slow mordent." At bar 8 the second minim
may be taken as either two chords in a bar, or as one, for there is no
harm in allowing the bass to touch the 2nd inversion of a triad so long
as it goes back to the note it left, or on to another note of the same
triad, before the chord changes. Bar 17 could not be written in three
parts if one was in second species and the other two in first unless the
middle part sang A, for only a first inversion is possible on F sharp,
the leading note of the scale. This would permit of a D in the middle
part, but D would make a 2nd inversion when the bass went to A.
When florid counterpoint is reached such bars as these are easier to
treat, for then the middle part could move to C, E, or F sharp on the
2nd minim. Implied 2nd inversions occur when the lower part, having
proceeded to the 5th of the chord established on the first minim,
leaves it by leap and not by step. The one exception is when it leaps
to another note of the same chord and the chord does not change, as
at bar 8. If it proceeds by step, as at bar 17, no harm is done. In
Ex. 113 at bar 2, the bass leaps from an implied 2nd inversion of the
triad of G to a note not belonging to that triad. Compare the bad
effect of this with bars 8 and 9 of Ex. 112. The 2nd minim in bar 3 is
an actual, not an implied 2nd inversion, for the bass leaps to E which
is a 4th distant from the A of the C.F. Bars 4 and 5 are examples of
two chords in a bar. The whole example is given partly to show the
bad effect of jerky and disorderly leaps in the 2nd species, and partly
to show how ugly an implied or actual 2nd inversion can sound.
Ex. 114 shows a better movement of the 2nd species.
Ex. US
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Ex. 118
Ex.114
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107. Consecutives with one note intervening are sometimes notice
able. At a moderate pace and in few parts they are heard most
distinctly on the first minim (Ex. 115). On the second minim they
can be detected when they are both harmony notes, 8ths sounding
worse than 5ths (Ex. 116). When one is a harmony note and the other
is not, they are less noticeable (Ex. 117). When neither is a harmony
note they are not heard at all (Ex. 118). Although consecutives with
one note intervening were written without compunction in the XVIth
century, the student should avoid those given in Exs. 115 and 116 in
strict counterpoint. The rules concerning exposed 8ths and 5ths given
in (33)-(35) apply to strict counterpoint of every species.
Ex.115
J i/j J
Ex.116
r r r
Ex.117
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Ex.118
^
108. In counterpoint it is unusual to allow two parts to commence
simultaneously, except in 1st species, just as it is unusual to find two
important characters in a play making their first entry together, for
they would not attract so much attention. Therefore, in 2nd species,
the counterpoint commences on the 2nd minim of the first bar on a
perfect or imperfect consonance of the tonic or dominant triad, but
obviously not on a perfect 4th. If the C.F. begins on the dominant, the
dominant triad or its 1st inversion should be used, otherwise an implied
2nd inversion of the tonic triad may result (Ex. 119). The exception
is when the exercise is in more than two parts with a part in 1st species
below the C.F. and above the part in 2nd species (Ex. 120).
In two parts particularly, and in three as far as possible, unisons
should be avoided on the first minims of each bar except the first and
COUNTERPOINT AND HARMONY
last.
12).
Perfect consonances also sound bare in two parts (Pars. 8, 10 and
No repeated notes are allowed in 2nd species.
This rule obliges the student to keep the parts moving. It applies
in all the species of strict counterpoint except the first, but in no other
form of music. In first species the long and weighty scmibreves can
occasionally be repeated without bad effect.
Ex.119
6 I '
4 implied
Ex.120
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109. The cadences possible in two parts arc limited in number.
C.F's. usually fall from supertonic to tonic at the cadence. If the C.F.
is in the lower part, this leaves us with only one harmony for the penulti
mate chord, namely the 3 on the super-tonic. The possible movements
of the upper part are given in Ex. 121. Ex. 122 gives another cadence
which may be used freely. As the triad on the super-tonic will not make
a final cadence when preceding the tonic triad, this example must be
classed as one of two chords in a bar. But as these chords have two
notes in common, and the part in 2nd species moves by step, the effect
is so smooth that this cadence may be used freely. If, however, both
parts approach the penultimate bar by similar motion, exposed perfect
5ths will result.
If the C.F. is the higher part, only the dominant triad or its 1st
inversion is available for the penultimate harmony (Ex. 128).
^ In cases where the cadence in the C.F. is made by the leading note
rising to the tonic there are four cadences with the C.F. below (Ex. 124)
but only two with the C.F. above (Ex. 125) unless two chords are used
in a bar which would give two more (Ex. 126). When the C.F. proceeds
from dominant to tonic at the cadence and the C.F. is below, the
cadences are easy (Ex. 127). But if the C.F. is above, only one, and that
an unsatisfactory one, is possible. The ungainly quality of this cadence
is due to the leading note leaping an 8th, which has almost the effect of
a doubled leading note (Ex. 128).
All these cadences may be used in minor keys except that marked
with an asterisk in Ex. 127, which would involve the leap of a dim. 4th.
The student in writing 2nd species to the C.F's. given in Section I,
should use only numbers 3 and 6 in each case for writing a counterpoint
above the C.F. on account of this awkwardness of the cadence.
110. In Exs. 129 and 130, the same C.F. is treated in six different
ways, three below and three above the C.F.
Ex.ISS
SECOND SPECIES
75
Ex.123
Ex.124
Ex.125
Ex.126
rl
Ex.127
*
Ex.128
"
Ex. 129, No. 1. The counterpoint leaps too frequently and covers
too wide a compass (a 12th). No. 2 shows an example of crossing the
parts. No. 3 has a more conjunct movement and is the best. No. 4
contains tautophony and ranges too much round the tonic.
Ex.129
C.F.
XXI
76
COUNTERPOINT AND HARMONY
I
Ex. 130. No, 1 has not sufficient conjunct motion. No. 2 ranges
too long round the tonic. A third part is added to the last four bars of
No. 8 to show the harmony. The note C is omitted from bar 9 as neither
C natural nor C sharp would fit very well with bars 8 and 10,
A part in 2nd species can now be added to any of the C.Ps. given
on pp. 23, 26 and 48, or to those at the end of this section.
X.
130
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SECOND SPECIES
77
y
Exercises on Section VI, in two parts.
Add to the CJF.'B given below parts for Soprano above, and either
Tenor or Bass below, all of which must be in the second species. The.
cadSce of No. 3 is inserted. That of No. 4 is somewhat sumlar.
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COUNTERPOINT AND HARMONY
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Second Species in Three Parts.
lll.s There is little to add to what has been said in Section V.
Only one part should be in the 2nd species. The doubling of weak
notes, such as m&jor Srds, and the consequent incomplete chords are
not so noticeable on the second minim as on the first. Vigorous part-
writing should be the first consideration, complete chords the second
(54*). The third part in semibreves must be interesting, not merely
a filling up. Repeated notes may occur in it, but the fewer the better.
There are six different permutations of the three parts, namely :
C.F., CJ\, 1st, 2nd, 1st, 2nd.
1st, 2nd, C.F., C.F., 2nd, 1st,
2nd, 1st, 2nd, 1st, C.F., O.K.
All these should be practised on each C.F., transposing it to convenient
keys for the voices selected.
Some of the cadences are given in Ex. 181 ; others will be found in
Exs. 132 and 138. These two examples arc worked on each of the six
combinations given above.
Ex. 132 (1). Bar 9 is an example of two chords in a bar, the 3
on D and the triad on.G.
Ex. 132 (2). The small notes give the better part, but make a
very big compass for the alto.
Ex. 188 (1). Bars 9-11 are a good example of the sacrifice of
complete chords for better part-writing, for the alto might have been
G in all three.
In these two examples there are only 14 places where all three
parts move in similar motion, Of these 12 are two positions of the
same triad or chords in the relationship of tonic to dominant or sub-
dominant, or vice versa (36).
Ex.131
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SECOND SPECIES
79
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COUNTERPOINT AND HARMONY
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SECOND SPECIES
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82 COUNTERPOINT AND HARMONY
Exercises on Section VI , in three parts.
Add an Alto in the First Species
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Add a Bass in the First Species
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_12 C.F.
namely ^ G.F. i for each of the two C.F.'s, supplying both parts.
SECOND SPECIES 83
Adda Tenor part in 2nd Species beginning as below Tune by Henry Lawes
A a 4 ' (1595-1662)
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84
COUNTERPOINT AND HARMONY
Complete the following,adding the missi ng parts,all in the Second Species
Tune, %su meine ZuversicM! j, Cruger
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SECOND SPECIES
85
Add a Bass part in the Second Species
C.F.
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86 COUNTERPOINT AND HARMONY
Work all six permutations on the following eight C.F.'s :
In C for Alto and Bass
I " I IP . ..
11
In Bt for Alto and Bass
In Bt for Alto and Bass
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In G for Alto and Bass
IiiD min. for Alto and Bass
155
tT
17
18
Add Sop. in 1st, Ten. in 2nd Species
Tune by S. Wesley (1766-1887)
Add Sop. in 2nd and Bass in 1st
Add Sop. in 1st and Ten. in 2nd
Add Ten. in 1st and Bass in 2nd
SECTION VII.
THE SECOND SPECIES APPLIED TO MELODIES AND
BASSES.
112. In decorating the harmonization, or rather the free counter
points, to be added to the melodies and basses at the end of this section
the student will be allowed freedom of choice as to where and where not
to move in two notes against one. The greatest help to that end is a
close observation of the pleasantest rhythms of life, for where these are
transmuted into music beauty is sure to ensue. Such rhythms have
both unity and variety. A journey along a flat road without variation
of pace or of scenery is, like the second species of strict counterpoint,
dull and monotonous ; it is only an " exercise.*' A walk in glorious
country where fresh and unexpectedly beautiful vistas open out round
each curve is like real, live music. On the other hand, a rush with a
jerky stop at the end of it is just as irritating in music as it is in a motor
or a train. It is like a snowstorm in July, meals at irregular hours,
or walking into a ditch in the dark. Busy, restless music, getting
nowhere, is exactly like the movements of a timid, fussy human being.
The aim should be to avoid monotony and lack of variety on the one
hand, and to keep from fussiness, absence of purpose and lack of unity
and continuity on the other. There should be plenty of movement,
but not always at the same point in the phrase, or in the same voice.
113. The following phrase (Ex. 134) consists of two sequential
sections. Let us see the effect of decorating it ; firstly, as in Second
Species ; secondly, by inserting passing notes at the same point in
each section ; thirdly, by placing the passing notes at a different
place in the second section from that in the first. The last version is
the best because the underlying sequence which gives it unity is clothed
with variety by the decorations. These are not inserted at the same
place in each section, for this would lead to the monotony of the first
and second versions. All parts should have this unity and variety of
movement, it must not be confined to one or two,
Ex.134
88 COUNTERPOINT AND HARMONY
114. Freedom of choice is allowed in deciding which note in a tune
or bass shall be treated as a passing note. The connection between
rhythm and phrasing, and harmonic change, treated of in Section II
will now be easier to achieve, because it is not necessary to harmonize
every note.
In deciding which notes of a tune are harmony notes and which
are not, the principles enumerated in Section II should be applied.
There is one rhythmic law that is of the greatest assistance the law
of the agogic accent Weight tends to slowness, lightness to speed. The
first three species of strict counterpoint may be compared to jumping,
walking and running. The first requires the most time between each
movement and the body comes to the ground with more weight than
it does in the others. Walking is lighter and also quicker ; in the last
and quickest the feet hardly seem to touch the ground. The accented
passing note is necessary to manoeuvre harmonic changes perfectly
freely, but no tunes are given in this section which cannot be adequately
treated without its help.
115. Like all laws those of counterpoint arc so framed that people
must keep on the right lines. But to be governed by the spirit the
imagination the inclinations is the only way to freedom. In strict
counterpoint, except in the First Species, repeated notes are not allowed,
so that the student must move his parts ; in the free counterpoint
exercises they may occur. It is hoped, however, that inclination will
not tend in the direction of stagnation, but that energy born of
enthusiasm will lead to free movement. There will then be no risk
of too many repeated notes.
116. It will now be possible for two or more parts to move together
in Second Species. Two parts may do so in three ways : (1) both by
passing notes in similar motion ; (2) both by passing notes, but in
contrary motion ; (3) one by passing note and one by leap to a harmony
note either by similar or contrary motion. Even in Section II they
could both leap to a harmony note without the chord changing.
(1) Both by Second Species in Similar Motion.
Similar motion in passing notes cannot take place when the two
moving parts start from a unison, 5th, or 8th, as consecutives would
result. This leaves us with the 3rd and 6th (and, of course, their com
pounds; the 10th and 13th). Similar motion can also take place when
the two upper parts are at the distance of a 4th. With the harmonic
material already to hand no part is ever at the distance of a 4th from
the bass. When the two upper parts thus move in consecutive 4ths
the bass is usually a 6th below the higher of the two, and also moves
with them in similar motion (Ex. 135 (a) ). The result is a string of
chords of the 6th (13), and is essentially harmonic and not contrapuntal.
When one of the notes composing the first of the consecutive 4ths is
an ornamental and not a harmony note, provided the time is fairly
quick, no hardness is noticeable (Ex. 135 (b) ). Where both are harmony
notes they had best be avoided, except in very quick rhythms
(Ex. 135 (c)). J H J
Two or three consecutive 3 chords, infrequently used, need not
of necessity destroy the independence of the parts, but this should be
PASSING NOTES IN MELODIES AND BASSES
89
the limit. If the examples are carefully studied it will be found that
cases where all parts move in similar motion are rare.
Ex.135
(*:
Si
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(2) Both by Second Species in Contrary Motion.
It is this type of movement that will give the best results, and
must therefore be studied most thoroughly. At present only one
ornamental note can be used between two harmony notes. Later much
greater freedom will be acquired. If the scales in contrary motion
in Ex. 136 are examined, backwards as well as forwards, bearing in
Ex.136
8 6
4975
1
7588
68 *8 6497
mind the facts (1) that the two parts about to move must start from a
unison, 3rd, 5th, 6th, or 8th, or the compound intervals corresponding
the 10th, 12th, or 13th, etc. ; (2) that they must reach a harmony
note in two steps, it will be found that :
when the two parts are a unison apart they may move in either
direction, but unless they diverge they will cross (Ex. 137) ;
when a 3rd apart they can only converge, and will even then cross
(Ex. 138) ;
90 COUNTERPOINT AND HARMONY
when a 5th or a 12th apart they can converge, but not diverge
(Ex. 139) ;
when a 6th, they can diverge, but not converge (Ex. 140) ;
when an 8th, they may do either, but cannot converge if the
lower of the two is the bass (Ex. 141) ;
when a 10th, they can converge only (Ex. 142).
Exl87 Ex.138
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Ex.139
Ex.140
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Ex.142
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It will be a helpful exercise to write the diatonic scales in contrary
motion, making them fit in second species by altering the rhythm of
each as occasion demands. They must begin either a 15th, 17th, 19th
or 20th apart when converging. In Ex. 143 the crotchet corresponds
to the semibreve of strict counterpoint, the quaver to the minim, but
any note may be taken as the unit. Write with a time signature and
finish on a strong beat of the bar.
(3) One by Passing Note and one by Leap to a Harmony Note
Either in Similar or Contrary Motion.
Passing discords will be more frequent in this type of movement.
If well used they will make the music more interesting, if clumsily
managed they will result in crudity. They must only appear by con
trary motion in the exercises in strict conterpoint without a C.F.
The following hints will be of assistance :
Criticise as an actual chord the combination of sounds at the
moment when the discord appears. What kind of sound has it ?
Thin, or rich ? Rough, or smooth ? Will the addition of another note
in second species in another part make it richer or smoother ? If that
note be added, will the passage be too lumbering or busy ? What
is the pace of the music ? Will the discord be heard for long ?
Ex.143
PASSING NOTES IN MELODIES AND BASSES
91
In Ex. 144 (a) the Soprano at the first chord leaps to F, a harmony
note, whilst the tenor moves by passing note, The actual notes
sounding are,
a thin chord. At the second chord the
soprano moves by passing note, the alto by leap to a harmony note,
the result is,
also thin. At (6) the addition of passing
notes to alto and bass at the first chord result in an often heard com
bination,
as is also,
the result of the addition
of a leap in the bass at the second chord. Pace is the criterion. If
the music were quick and light there would be enough movement in (c).
The version at (d) would be better at a dignified pace, while (e) would
make quite a good, broad climax. Note the effect of the " slow
mordent " in the tenor at the penultimate chord,
This
example is given partly to show the infinite variety to be obtained
even with the slender resources acquired at this early stage, and also
to impress once more on the student's mind that in music you cannot
decide whether a thing is good or bad by one consideration alone.
The laws of rhvthm and motion are the final arbiters, and not harmony.
Ex.144
(a)
92 COUNTERPOINT AND HARMONY
..Andante
A discord will stand out much more when approached by leap
in similar motion than by step. This has already been proved
to be the case with perfect concords (33), it is still more so with
discords. There is no harm in the discords themselves, quite the
reverse, if the laws of rhythm are obeyed. At present the only places
where discords may occur are at weak points of the rhythm, and if
these points are made too prominent by placing strong discords on them,
reached through large leaps, the rhythm will suffer (Ex. 145).
Ex.145
Avoid 9ths (as well as 7ths) moving by similar motion to
8ths, and 2nds moving to unisons. These are only possible when
two or more parts move together. They are common in modern
music, and in many cases are harmless, but they had better be avoided
for the present (Ex. 146).
Ex.146
It need hardly be said that the passing note is not always of the
same length as the previous harmony note except in strict counterpoint.
The former may be a third or half the length of the latter, but the
harmony note, being of the greater importance, should never be shorter
than the passing note (114). When two parts move they need not do
so in notes of the same length as long as they reach the next harmony
note together. Ex. 147 (a) shows the unit corresponding to the semi-
breve of strict counterpoint in superimposed notes. In the first bar
the soprano passing notes are semiquavers, the bass quavers. In
Ex. 147 (b) the harmony notes are crotchets for the most part, and the
passing notes quavers, the dotted crotchet being the unit.
PASSING NOTES IN MELODIES AND BASSES 93
Part of Irish Tune 'The Gentle Maiden 3
Ex.147 J. J. J
Part of Irish Tune '
j ^ J ^ J.
117 The customary relaxations may be made from strict coun
terpoint with regard to horizontal intervals (N.B. at end of_(80)).
Even the leap of a 7th may now be made provided it conforms to what
was said in (29). The quicker the movement the smoother it should
be " Passage work," towards which the second species is the first
step, is smooth when it moves either as a scale, or as an arpeggio.
Such a passage as Ex. 148 is not smooth, because it suggests neither.
It is not wrong; at a moderate pace with a sympathetic context it
might sound quite fanciful.
S Ex.148
118 The same unit need not always represent the semi-breve of
strict counterpoint. In Ex. 149 at the points marked (a) the minim,
and at (b) the crotchet, is the unit.
Ex.149
(ft
119 A common mistake is to forget that the balance of a chord
has been altered when one part has moved from its original position;
and that if the rhythm will allow it, it is often better to move others
to restore the balance. In Ex. 150 (a) when the soprano moves to
B flat the chord has a doubled 5th and no 3rd. In nine cases out
94
COUNTERPOINT AND HARMONY
ten either (b) or (c) would be the better versions. In the tenth case
(d) would be best, for here the time is quick and the unbalanced chord
too light to be noticed ; and if all three parts moved the rhythm would
be clogged.
Ex.150
(^Allegro
J^
120. Four examples of tunes with two parts added in free counter
point are appended.
Example 151, Out of 32 chords 20 are complete. Of the 12
incomplete, 5 occur either at the beginning or end of a phrase.
Bar 1. The exposed 5ths are not ugly because the roots of the
triads are a 4th and a 5th apart. This is a sufficiently strong relation
ship to warrant the familiarities mentioned in (37), even when one triad
is minor, as at the 2nd crotchet.
Bar 3. The F sharp in the bass on the 3rd crotchet is a leap to a
harmony note. It is not movement for the sake of movement for it
is never well to stop an upward movement just before it reaches the
top of the wave.
Bar 6. The passing discord of the 9th on the 2nd quaver is not
too hard even though it is approached by similar motion ; the soprano
and bass move too smoothly for that. This type of movement must
not be used in strict counterpoint. The crotchet is the unit representing
the semibreve of second species throughout.
Ex.151
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PASSING NOTES IN MELODIES AND BASSES
Example 152, The Chorale was originally in the Dorian mode,
the notes of which correspond to the scale of D minor without B flat
and C sharp. The addition of accidentals has robbed it of its modal
flavour except that it appears to us to begin in A minor and finish in
D, and still retains the key signature of the Dorian mode, i.e., C. At
bars 4, 6 and 8, second half of second beat in each case, the quaver
becomes the unit, the semiquavers representing the minims of second
species. If these occurred once only they might sound odd and lonely
(variety without unity).
Bar 7, first half. The minim is here the unit. C sharp is a " slow
mordent " inverted. G in the tenor and E in the bass are passing
notes. In bar 3, second beat and bar 11, second beat, one note of the
tune is given two chords corresponding to the u two chords in a bar "
of strict counterpoint.
Bar 4. Note the proximity of the 5ths (Ex. 117).
Ex.153
Chorale, Christ laginTodesbanden'
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Example 153, Although the melody moves in quavers it is better
to keep the crotchet as the unit and treat the repeated quavers in the
tune as if they were tied. If every quaver were a harmony note the
effect would be too lumbering. The tune is in the Mixo Lydian mode,
96
COUNTERPOINT AND HARMONY
5
Later on the question of the modes will be gone l
the , meantime for a folk song keep strictly to the notes
The parts slurred in the tenor and bass would not be good
Ex 158
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JFng-ZtsA Folk-Smtf 'The Banks of the Sweet Ihuulee'
Example 154, In order that the analysis of the bars at (a\ (
* bete *" they " bee " ^nbS'r?^
Ex. 154
JT^r/tsA Mk-8o*f 'Tie Crystal Spring'
(Copyrjght)
PASSING NOTES IN MELODIES AND BASSES 97
Exercises on Section VlL
The first three exercises are skeletons of tunes, like Ex. 134 (a).
Clothe them with ornamental notes of all three kinds, namely, slow
mordents, passing-notes and leaps to harmony notes, Vary the rhythm
by adopting various units to represent the semibreve, and usino- dotted
notes. e
1 1 1
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98
COUNTERPOINT AND HARMONY
Decorate all three parts of the next three exercises with ornamental
notes.
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Examine Example 147 carefolly before doing Exercise 6.
PASSING NOTES IN MELODIES AND BASSES 99
Write the next eight exercises in strict counterpoint except that
there is no semibreve C.F. The minim is the unit, throughout Use no
quavers, otherwise the rhythm of all parts is quite free. Repeated
notes may occur occasionally.
Complete Nos. 7 and 8 by adding a tenor to No. 7 and an Alto to
No. 8 beginning as indicated below.
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100
COUNTERPOINT AND HARMONY
Add whatever parts are missing in the next six exercises.
te
PASSING NOTES IN MELODIES AND BASSES 101
Write two parts below the Chorales given in Nos. 15, 16 and 17.
Passing discords may now occur when one part moves by passing-
note and the other by leap to a harmony note. The intervals mentioned
in (117) may now occur horizontally.
15
Chorale 'Ss ist das Heil uns Kommen her'
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Chorale ( Vater unser in, JIinim,elreich'
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Chorale 'liebster Jesu*
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102
COUNTERPOINT AND HARMONY
Add two parts below the melodies given in Nos. 18-21. The trwit
ment may be freer. See note to Ex. 153.
19
Andante
Rosseter (l60l)
Old Irish Air
(Copyright)
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PASSING NOTES IN MELODIES AND BASSES 108
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SECTION VIII.
SUSPENSIONS. THE FOURTH SPECIES OF
COUNTERPOINT.
121. Just as one may imagine that the passing note first came
into music through some singer slurring or scooping, that is, filling
in intermediate sounds an effect dear to the heart of the average
songster so the suspension must surely have originated through one
performer getting behind the rest another sin to which singers are
still prone. So that what was meant to sound like Ex. 155 (a) sounded
like Ex. 155 (b).
Ex. 155 (a) ' (b)
A beginning was made in the last section with the study of passing
discords. Fourth Species is the introduction to accented discords. As
it opens out a new channel, gives a much more comprehensive and
interesting vocabulary to the student and is quite easy to understand
and to practise, it should come before Third Species. This is a develop
ment of the Second, and not required nearly so often as Second and
Fourth.
Dissonance in music expresses energy to work and accomplish
something. As one of the most satisfactory feelings in life is the
knowledge that really good work off one's own bat has been accom-
lished, opposition overcome and repose well won, so discord in music
gives it strength and vigour, and the resolution of the discord where
it melts into the concord gives to that concord a raison d'etre it could
never have had without the discord. But as in life periods of rest are
short-lived, and hard work is a panacea for all ills, so in music ; for it
will soon be realized that not only do discords and their resolutions
succeed one another at short intervals, but that one discord often
resolves upon another.
122. The suspensions of strict counterpoint have three periods
Preparation, Percussion and Resolution.
Preparation. A note about to be suspended must first appear
as one of the harmony notes of the previous -chord. That appearance
must be in the same part as the following suspension. In strict counter
point the preparation is tied to the suspension, but in the freer style
om
FOURTH SPECIES
105
suspensions may or may not be tied. The tying and the preparation
make for greater smoothness, like most contrapuntal rules. To give
a suspension its best rhythmic effect to make it eager enough and of
sufficient importance the preparation should be a note as long as
(Ex. 156 (a)) or longer than (Ex. 156 (b)) the percussion ; not a shorter
note (Ex. 156 (c)). This applies to all tied notes in counterpoint,
whether suspensions or not.
Percussion. This is the actual moment when the discord is
struck. It should occur at as strong (or stronger) a rhythmic point
in a bar as the preparation, but never at a weaker point.
Ex. 156 (a) (b) (c)
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Resolution. This is the fall of the discord one step to a harmony
note of the triad established at the moment of percussion. Discords
are either Passing or Accented, Prepared or Unprepared ; resolved
before the moment of harmonic change, or resolved after that point.
The suspension of strict counterpoint is Accented, Prepared and resolved
before the moment of harmonic change. The old rule called it a resolution
whilst the rest of the chord remained stationary. This was not quite
accurate, for the rest of the chord, or part of it, may move either to
.another inversion (Ex. 157 (a)), or in ornamental notes (Ex. 157 (b)),
but not to a chord of another root (Ex. 157 (c)), except in the case of
the particular type of suspensions explained in (135).
Ex. 157 (a) (b) (c)
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The Suspension of each of the notes of the Triad and its
First Inversion.
123. As the only chords used in counterpoint are the triad and its
first inversion, the suspension of the notes of these chords is the only
type treated of in this section. Later on it will be seen that practically
any note, dissonant or consonant, may be suspended.
The Triad. Suspension of the 5th (Ex. 158 (a) ). This differs
from the other suspensions in that it has no actual discord, but sounds
like a | followed by a triad on the same bass note. It is used freely
in Fourth Species.
* It is not usual to figure the 3rd of the chord. The usual figuring for suspensions
is abbreviated to 4-3, 7-6, 9-8, etc.
106
COUNTERPOINT AND HARMONY
Suspension of the 3rd (Ex. 155 (b) ). This is perhaps the
commonest of all suspensions and is -beloved of the village organist in
his improvisations.
Suspension of the root (Ex. 158 (b) ). The bass being the most
important part, suspensions of it give great strength to the music.
The First Inversion, Suspension of the 6th (Ex, 156 (a) ).
The next in order of frequency to the 4-3.
Suspension of the 3rd (Ex. 159 (a)) . As the 3rd of the | is
the 5th of the original triad, this comes under the same head as that of
the 6-5 suspension (Ex. 158 (a) ). It is, however, very slightly more
dissonant since it contains a 4th with the bass.
Suspension of the bass (Ex. 159 (b) ). This has a similarly strono-
effect to Ex. 158 (b).
Ex.158 (a) (b)
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124. It will be noticed that in none of these suspensions is the
note doubled upon which the suspension will resolve. Thus, in
Ex. 158 (a) the note of resolution, G, is absent from the other parts.
Likewise in Exs. 155 (b), 158 (b), 156 (a), 159 (a) and 159 (b), the notes
B, C, C, G, and E, respectively, are omitted from the chords. Speaking
broadly, the note of resolution may be doubled when such doubling
would not have been objectionable without a suspension, but there
are two important reservations to this : (1) where the doubling of a
suspended note would make for ambiguity or lack of clearness in the
part-writing ; (2) where the doubling would intensify the discord so
much that it would be too strong for strict counterpoint. In Ex. 160 (a)
there is no objection to the doubled root in the second chord, therefore
in 160 (b) the suspension of that note is harmless. This gives us the
suspension of the 9th, one of the commonest of all. In Ex. 161 (a)
there is no reason why soprano, alto and bass should not sin* C in the
second chord, but if the C is suspended, as at 161 (6), the resolution
ol the 2nd between soprano and alto is not satisfactory, for it might
be taken as at 161 (c). This example sounds just the same as 161 (b)
except that in 161 (6) the soprano and alto sing a unison at the weaker
hall ol the bar. The individual movement of the parts is therefore
FOURTH SPECIES
107
ambiguous. The 9th, along with other compound intervals such as
the llth, and 13th, may be treated as a 2nd (the llth as a 4th, and
the 13th as a 6th). On the other hand, each of these intetvals may
be given a character and status of its own, in which case these intervals
are quite unlike the 2nd, 4th and 6th. If the interval is a 2nd, the
resolution is usually effected by the lower of the two notes descending
one step, but if it is a 9th, it is resolved in exactly the opposite way
the upper note descends. It is the harmony that settles the question
as to whether the interval is a 2nd or a 9th. Thus, in Ex. 159 (b),
the apparent 9th between the bass F and the alto G is really a 2nd,
for the harmony is a first inversion on E with the bass suspended, and
the' notes of the chord are E, G and C. In Ex. 160 (b) there is a real
9th between the C of the bass and the D of the soprano, for the harmony
is a triad on C with the root doubled and suspended by the soprano,
whose D stands instead of C and will resolve on that note.
Ex.160
In Ex. 162 (a) there would be no objection to the doubling of the
major 3rd in bar 2, for the parts pass through it by contrary motion
and by step. But if the soprano were suspended, as at (b), there would
be a considerable clash which could be avoided by making the tenor
sing D, as at (c). There are other factors in the case, as follows :
(1) The suspension of a doubled bass note is better than any other.
The suspension of a doubled note between two of the middle
or upper parts makes for a thinner effect and a stronger
dissonance.
(2) Intervals vary in degree of dissonance. The minor 2nd,
major 7th and minor 9th are much more pungent than the
major 2nd, minor 7th and major 9th. It has already been
pointed out that the suspension of a doubled note intensifies
the dissonance. If it also incurs the use of one of the former
three intervals (minor 2nd, major 7th or minor 9th), the
dissonance is still further intensified.
(3) The character of the motion of the two parts concerned in
the suspension affects the situation. Contrary motion by
step tends to lessen, similar motion by leap to intensify,
the dissonance.
108 COUNTERPOINT AND HARMONY
Ex. 163 ( fl ) (b) (c)
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Where all factors tend to smoothness, when the doubling would
have been unobjectionable had there been no suspension, where the
part- writing is clear and the movement in contrary motion and by step,
where the suspended interval is one of the second group mentioned
and where that interval is between the bass and an upper part, naturally
a very harmless effect results. There may be one, two, or three of
these "factors which do not help to smoothness ; the dissonance is then
strengthened in proportion.
The following cases of doubled notes suspended are harmless :
(1) All 9-8 suspensions when the bass is the root of the triad
(Ex. 160 (b) ).
(2) All 9-8 suspensions wh'en the bass is the 3rd of a minor triad
(Ex. 363 (a) ). This involves the use of the major 9th.
(3) Suspensions of the 9th when the bass is the 3rd of a major
triad so long as the two parts concerned pass through the
suspension by contrary motion and by step (Ex. 163 (b) ).
This involves the use of a minor 9th.
(4) Suspensions of the root of a triad in the bass when the note
of resolution is doubled in an upper part (Ex. 163 (c) ).
This suspension is smoothest when the two parts approach
it by step in contrary motion, but the progression is almost
as smooth when the upper part leaps by a small interval
(Ex. 163 (d) ). Even if the upper part approaches by similar
motion the effect is not uncouth (Ex. 163 (e) ). Later, when
passing notes and suspensions are combined, it will be seen
that the suspended note may be doubled by another part
moving through it in passing notes by contrary motion
(Ex. 163(/)).
(5) Any other suspension of a doubled note in a chord, so long as
the suspension is limited to the suspension of a doubled
root between the upper parts ; the part not suspended
to approach by contrary motion and by step (Ex. 163 (g) ).
Ex.163 (a)
(b)
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FOURTH SPECIES
109
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125. Consecutives. The academic rule that which is wrong
without a suspension is also wrong with one scarcely holds good
with regard to consecutives. Ex. 164 contains consecutive 5ths
between soprano and alto. The version at (a) differs only in that the
second 5th is suspended and thus its appearance is delayed until the
weak half of the bar. Many such cases can be found in music of all
time (see Exs. 165-6). The 5ths can be heard, and those who
dislike the effect of them can easily avoid them. They are not tolerated
in strict examination counterpoint. In the later sections, when it
will be possible to move the parts more freely, it will be found that this
movement, together with any other dissonances present in the harmony,
tends to distract the ear to draw a red herring across the path and
the 5ths are not so noticeable (Ex. 164 (b) ). When the unsuspended
part, which would have caused the consecutives had there been no
suspension, moves away to some other note at the moment the
suspension resolves (Ex. 164 (c)), and the second 5th is never actually
sounded, there is no effect of consecutives ; although when the author
went to school even this was taboo. Consecutive 5ths with one note
intervening, where one of the sounds is a suspended note (Ex. 164 (d))
or where both are (Ex. 164 (e)), are harmless (107).
Suspensions which would have resulted in consecutive 8ths, had
there been no suspensions, are another matter. There is not usually
sufficient independence of movement or of sound to make them worth
while.* The only exception is the one corresponding to Ex. 164 (c),
where the unsuspended part moves away before the resolution. This
is harmless just because the independence of the parts is not sacrificed
(Ex. 164 (/) ).
As consecutive 3rds and 6ths are innocent, they are quite common.
Naturally therefore, consecutive suspensions of these intervals (4-3
and 7-6) are also common. In working exercises in the Fourth Species,
if the C.F. descends in steps and the first suspension is a 4-3 or 7-6
over it, or a 2-3 or 5-6 beneath it, the suspensions must of necessity
continue until the C.F. leaps (see Exs. 171, bars 5-7, 176, bars 6-8).
Ex. 164
*See Ex. 201 (a) in which Talhs breaks this rule with good effect.
110
COUNTERPOINT AND HARMONY
(/)
SE
Ex. 165 Palestrina (1525-1594) (Stabat Mater}
Ex. 166
Byrd (15J8-16231 ('Songs of Sundry Natures')
126. The exercises on semibreve C.F.'s given at the conclusion of
this section are the most rapid and intensive method of familiarizing
the student with suspensions and their use. They are too monotonous
to be very musical, but are as useful as other mechanical exercises in
music. The counterpoint should begin on the second minim of the
first bar. Each second minim should be tied to the first minim of the
next bar. This may be either the percussion of a suspension, or the
tying of the harmony notes common to two contiguous chords.
In academic counterpoint the student was allowed to break the
syncopations here and there and introduce a bar of Second Species.
This was done to get out of some impasse and often tempted the student
to avoid using his ingenuity to the full extent. All the C.F.'s given
below can be worked without any break in the tied notes except at the
penultimate note of the cadence. This may occasionally be a passing
note when the suspensions are not in the lowest part, and the dominant
falls through the sub-dominant to the mediant (Ex. 168 (a) ).
Two chords in a bar may be used when they are both on the same
bass note, the first being a triad, and the second a 3. In the XVIth
century this often caused consecutives with one note intervening
(Ex. 167). This is a useful device at the cadence when the Fourth"
Species is above the C.F. (Ex. 168 (b) ). The B flat in this example is
to avoid the tritone at bar 3.
In two parts too many 9-8 and 6-5 suspensions are nearly as thin
in effect as too many perfect concords in the First Species (47 (3) ).
It is important to start on the most convenient note, and to watch
for places where there is more than one option. For instance, in
FOURTH SPECIES
111
Ex. 172, bar 9, the chord might have been taken as an implied |
and a leap made to C on the second minim had that been a more con
venient arrangement.
Ex, 167
Byrd ('Songs oj Sundry Natures')
^=4
Ex 168
The skip of an 8th is often useful and necessary. (See Ex. 176,
bar 9 ; Ex. 178, bar 6, etc.)
The commonest cadences are as follows :
When the suspensions are in an upper part
A 7-6 on the super tonic. (Exs. 169, 171.)
A 4-3 on the dominant. (Ex. 177.)
A 7-6 on the leading note. (Ex. 174.)
A 5-6 on the super tonic. (Ex. 168 (6).)
A passing note. (Ex. 168 (a).)
When the suspensions are in the lowest part
The suspension of the bass of a 3 on the leading note.
(Exs. 172, 178.)
The suspension of the bass of a dominant triad. (Ex. 176.)
Ex.169 _
*
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112
COL
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Ex. 171
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Ex. 174
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Ex.175
MU^
XH
FOURTH SPECIES
113
Ex. 176
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Exercises on Section VIII.
Add a Soprano in the 4th Species, beginning on C
C.F.
:i=
Add a Soprano in the 4th Species, beginning on A
C.F. i o
114 COUNTERPOINT AND HARMONY
Add an Alto in 4th Species, beginning as indicated
ax:
C.F.
33=
Add an Alto, beginning as indicated
C.F.
TF
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Add an Alto in 1st Species, beginning as indicated
C.F.
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6. Transpose the C.F. of N9 5 a 4th lower into the Key of C, giving it to
the AKo. Add a Soprano in the 1st Species. Use the same bass as N95
transposed a 4th lower.
Add a Soprano in the 4th Species
Add a Soprano in the 4th Species, beginning as indicated
C.F.
JQL
FOURTH SPECIES
Add an Alto in the 4th Species,beginning as indicated
115
ll * " 1
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Add an Alto, beginning as indicated
10
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Adda Tenor in 1st Species, beginning as indicated
C.F.
Give the C.F. of N9 11 to the Tenor and use the same bass. Add a Soprano
in 1st Species.
The following C.F.'s can be worked without breaking the synco
pations, whether these are above or below them. Write them first in
two and then in three parts, transposing them to keys convenient to
the voices selected.
116
COUNTERPOINT AND HARMONY
From a, Tune by Tallis (1505-1585)
15
" I o
" =5
32=
18
SECTION IX.
FOUR-PART WRITING.
127. Those who feel that they can handle two or three horses with
comfort may now learn to drive a four-in-hand.
There is practically nothing to add to what was said in Section V.
The advice given in (102 (4)) to avoid a diminished 5th, followed by
a perfect 5th, may, however, be relaxed as regards the two inner parts
(see Ex. 182, bars 3 and 4). Unisons may occur more frequently than
in three parts either on the strong or weak parts of the bar.
128. When two major triads follow one another the roots of which
are a semitone apart, as are the roots of the submediant and dominant
triads in minor keys, there are so many augmented and diminished .
intervals between the notes of these triads that the progression of
each part is practically arbitrary. It will be seen from Ex. 179 that
an augmented 5th or its inversion, the diminished 4th, lies between
the 5th of the triad on the upper note and the 3rd of the triad on the
lower one ; that an augmented 2nd lies between the root of the upper
and the 3rd of the lower, and that an augmented 4th or diminished
5th lies between the root of the upper and the 5th of the lower triad.
In four-part writing it will be found that unless the third of the upper
triad is doubled, either consecutives, or an augmented, or diminished
interval will occur in the progression of the parts between these triads.
To take each part in Ex. 179 (6), the bass is fixed ; the tenor, which
has the leading note, G sharp, naturally moves to the tonic, A. But
if it did not do so it could not move to the 5th, C, because of the
diminished 4th or its inversion, nor could it move to the root, F, because
of the augmented 2nd. The third, A, is the only note available. The
doubled root, E, in the alto of the first triad has apparently two
options ; it may either move to the 5th of the next triad, C, or, may
go to the 3rd, A. If it did the latter, however, there would be no 5th
in the second chord, for the B in the soprano could not go to C by reason
of the consecutive 5ths between the bass and soprano. In fact, A is
the only note possible for the B ; for F, the only other note, is separated
from if by the interval of an augmented 4th or its inversion. Thus,
this progression is arbitrary. Ex. 179 (c) shows the triads in the other
order. It is in this position that the majority of mistakes occur, for
students forget to double the major 3rd in the first triad.
Ex. 179 (a)
Ex. 179 (b) Ex. 179 (c)
^J/L
,
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118 COUNTERPOINT AND HARMONY
129. At first it may be difficult to make all four parts interesting.
One or two will evince a tendency to hang about witli their hands in
their pockets. To overcome this, train the mental ear to hear and the
the mind to visualise a few bars ahead. The distance for which this
can be done will increase with practice. . When writing do not get
ahead with one part by itself, but write the whole four' together.
130. It will be noticed that doubled major 3rds (1)*, overlapping
of parts (2), and leading notes which do not rise immediately to their
tonics (3), or do not rise at all (4), are included more often than in most
counterpoint examples* There is usually sufficient excuse in the
progression of the parts. There are also a few places where individual
parts break the Palestrina rule given in (29). In four-part writing when
only semibreves and minims are used this is sometimes unavoidable
except by repeating a note or by tautophony. Later, when the semi-
breve C.F. has been dispensed with and freer rhythms have been
adopted, the rule can be more faithfully followed.
Such imitation as is found in Exs. 187 and 191 should not be
attempted unless it comes along easily. Time spent in labouring such
devices is wasted.
Two examples are given (184 and 185) of melodies from Section II
harmonized in four parts without passing notes. Observe the effect
of the points enumerated below.
(1) Consecutive 5ths with one note intervening (Ex. 184, bar 1,
alto and tenor ; bars 9 and 10, soprano and bass, and tenor'
and bass ; bar 14, soprano and bass ; bar 15, soprano and
alto ; Ex. 185, bars 7 and 8, alto and bass).
(2) " False relations " with one note intervening (Ex. 185 bars 2
and 7). (See (85)).
(3) The frequent use of triads and their inversions on every note
of the scale, not relying too much on tonic, dominant and
subdominant. In Ex. 184 chords from the root E flat
are used 17 times ; from F or F sharp, 9 times ; from G,
12 times ; from A flat or A natural, 11 times ; from B flat,
13 times ; from C, 11 times ; and from D or D flat, 7 times!
It is obvious that, however well they are done, such restricted means
can only lead to a more or less unsatisfactory result. Too frequent
harmonic change results in a heavy, forced movement. On the other
hand, if the chords change too seldom, or if the changes are rung on
two or three chords, monotony and a feeling of movement for the sake
of movement may result. More will be said on this subject later on
It is none the less important that these exercises should be done for
there is no greater law in art than the law of economy he who does
the best work, does it the easiest way and with the least use of material.
paraph figUrS ^ ^^^ t0 bef Und iU EXS ' m i0 191 refeY to th& fi^es in this
J?UUJt-rAKT
Ex.180 First Species in four parts.
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Ex. 183
St. Mary. From flay fords Psalms (167?)
at
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120
COUNTERPOINT AND HARMONY
Ex. 184 Melodies harmonised with triads and their 1st Inversions only
German Chorale 'fferzlick thut mieli erfreu,en>
Ex. 185
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FOUR-PART WRITING
Ex. 186 Second Species in four parts.
121
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122
Ex. 191
COUNTERPOINT AND HARMONY
St. Mary
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XE:
FOUR-PART WRITING 123
Ex. 192 Melodies with passing-notes. , , ,
t v & *. German Ch&mle ( r ist das Seil*
At first sight it would look as if the chord of the dominant 7th had
been used in bars 4 and 6 in Ex. 192, but on analysis it will be found
that in bar 4 the chord of B prevails through the 3rd and 4th beats,
and, as the alto and tenor do not leap and continue in the same direction
to the next harmony notes, they are moving in passing notes. In
bar 6 the chord of C sharp is not changed until the 3rd beat. The
soprano moves in crotchets, the B is a passing note. The F sharp and
D sharp in alto and bass respectively are quaver passing notes, and
the leap to the C sharp in the tenor is a leap to a harmony note (116).
Ex. 193, last bar, contains a cadence which should be analysed.
Here there are no leaps, the whole effect being obtained with passing
notes.
Ex. 193
Irish Melody (Aflolian Node, transposed)
124
COUNTERPOINT AND HARMONY
EX.194 Fourth Species 'Wieschon leuchtetderMorgenster J.German Chorale
C.F. ___^
33=
C.F.
33=
33=
FOUR-PART WRITING
125
^
C.F.
C.F.
if =30E
30=
- r
O
C.F.
AI o -e
32=
3O=
C.F.
126
COUNTERPOINT AND HARMONY
r-g-r- -i
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C.F.
o "-u
22=
/7s
Exercises on Section IX.
I. Add an Alto and Tenor, note against note.
C.F.
1 Menschjbewein? dein Surute grosi-
German Chorale (Original form)
^
T^ *
S
i. Transpose the C.F. a 5th lower, put it in the Alto, nse the following Bass
and add Soprano and Tenor parts.
"it 1 jj! lj jr' '
FOUR-PART WRITING
127
3. Write the C.F. in the Tenor in the Key of F. Use the following Bass, and
add a Soprano and Alto.
IrrNMI
4. Add an Alto and Tenor.
^j
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fj p *~f- f. fiy ^
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5.
Add
56 5-
33
Alto and Tenor.
=f=f=t=f
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656
Vafer unser. Chorale
: -T-r tE T f fr=F=
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128
COUNTERPOINT AND HARMONY
XT'
6. Transpose the C.F. a 4th lower, put it in the Alto. Use the Bass given
and add Soprano and Tenor.
7. Pat the C.F. in the Tenor in D minor. Use the given Bass. Add Soprano
and Alto.
if r.J'l
666
566
8. Add Alto and Tenor.
9. Add Alto and Tenor.
Somersetshire Folk Song, 'Sovay^Sovay* (Copyright)
FOUR-PART WRITING
129
10. Add Alto and Tenor.
Somersetshire Folk Song in the Dorian Mode'Henry Martin' (copyright)
11. Add three paits to any of the C.Es. given in previous Sections, all in first
species.
Add three parts above the figured basses given in Exercises 12, 13 and 14.
! I
6 6
6 6 56
6 1)6
r i
5 6
When the bass has a note of more than one beat's duration the upper
parts may move, but only to notes belonging to the chords indicated
130 COUNTERPOINT AND HARMONY
In the Phrygian mode.
665
1 1 _..
656 6 IT
nr i i n '
6 566
66 6 6
6666 66 6 656 6 66 # #6
m
6 5
6 6 # 6 66
Add -three parts above the nnfigored basses ia Exercises 15, 16 and 17.
16=
jj.ij.-r
FOUR-PART WRITING
131
Complete Exercises 18 and 19 in strict counterpoint by adding the miss
ing parts.
2nd Species
Tune by Henry Lawe*
Mr /IT i i i
1st Species
C.F.
"
C.F.
I I " I
1st Species
n
1st Species
1st Species
C.F.
o i *i-
|o
* , C.F.
Jf \\* . ~ Q' I l._ I *>* f o I -A I i ~ j ~" " ~ r -'-- ._
$* a \ I " I I I " I " I II
1st Species
2nd Species
^
COUNTERPOINT AND HARMONY
Tune Jrom, Play ford's Psalms (l67i)
19
MM I
1st Species
f^ n ,- i ry
C.F.
^
i
1st Species
1st Species
C.F.
nn
-rr-
^
C.F.
FOUR-PART WRITING
133
20. Add an Alto in 2nd Species and a Tenor in 1st.
A C.F.
"JBrt "
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o
o
tr "
p .... .
o
Add a Soprano in 2nd Species and a Tenor in 1st
C.F.
22,
Add three parts to any C.F. previously given.
in 2nd Species.
One part should be
131. Notes to the Exercises.
No. 8. This contains a chromatic progression (bars 2 and 3). It
is found in XVIth century music, where it often occurs, as it does here,
between the last chord of one phrase and the first of the next. Hori
zontal intervals which would be uncouth in the middle of a phrase can
often be permitted in this position, for, after a cadence, the music more
or less begins afresh.
No. 14. The free exchange of 4 for 2 time is also is accordance
with XVIth century usage.
No. 19. Bar 10 contains two different chords, for, as a leap is made
from the E in the soprano, it cannot be a passing note.
Exs. 195 and 196. These are excerpts from Palestrina ; Ex. 195
from the Credo of the Mass, Assumpta est Maria, Ex. 196, from the
Benedictus of the Mass, sacrum Convivium. With the exception
of the suspensions, marked with an asterisk, they contain nothing
contrapuntally or harmonically beyond the knowledge of the student
at this point. But they require careful analysis before they can be
taken as models, and exercises written on the same lines.
In Ex. 195 the minim corresponds to the semibreve of academic
counterpoint. Single, unaccented, crotchet passing notes are used
throughout, except at bar 12, 3rd and 4th minims, where the semi-
breve is the unit. The form is a common one with Palestrina and
composers of his period. A purely note-against-note section is followed
by points of imitation. The first point begins at bar 5, the second
at bar 10, this carries on to the end. The close of each section is marked
by a cadence.
Exercise 23 is written on the same lines, but things are made easy
for the student by giving the themes for imitation, and by omitting
suspensions and only using one passing note between harmony notes.
When these have to be invented, as in Exercise 24, it will be found that
the more strictly the rules given in (29) are kept the easier it will be to
make the imitation fit. Conjunct motion, or small leaps, few chord
changes and an interesting rhythm, as in the Palestrina example, are
134
COUNTERPOINT AND HARMONY
the "things to be aimed at. The words are not obligatory, but they
suggest rhythms and give point to the repeated notes. Either Latin
or English words may be used. The former will probably present fewer
difficulties of accentuation, and the latter will suggest a greater variety
of rhythms.
,Ex.l95
Palestrina
Bt i - ter-um yen - tu-rns est um glo - ri-a ju-
- di-ca - re
vos et mor
ta-
m
^^
vos et mor
ta-
^
3X2
vi
vos et mor - tu -
A
J - 8
vi - vos et mor - tu -
9
10
11
[^ ^
ZT" '
IT ?r
|^ 1 r J 1 1 1 J r f f f- 1
ft=
I " M
os: cu - jus
lf~ P~j
N> i ^ I s ** i j ^ * [ r i i 1
re - gni non e - rit fi
s=*=
os: cu - jas
JTfl - CTTli Tinrt a ri +
f^
IS) "
p^
os:
ca - jns re gni,
KHZ---
dt [ i
i ' t 1 n if 1 1 r^^
-os:cu~jus re - gni none -rit fi
12
FOUR-PART WRITING
13 * 14
135
15
*
nis, cu - jus re - gni_
if
fi
nis,cu - jus re - gni non
cu - jus re - gni non
- nis, cu - jus re
18 19 20
=W=
non e-rit fi
nis.
fl ,1 *
1^
W=
e-rit fi
nis, non e-rit fi
nis.
e-rit fi
nis, non e
lit fi - nis.
F3=
none -lit fi
nis.
23. Fill in the missing parts, taking Ex.195 as a model.
J lo J
And He shall come a - gain with glo - ry, shall
r J> J i j J r7 r i r ^
136
COUNTERPOINT AND HARMONY
pp
J
P==
I - J J J J=p=
J
come a-gainwith glo - ry
_ *=*_
_ J 5-^ ff j
to judge boththe
r"> r * f
f
N
9
1
i=t=
r r r 1
judge boththe q^nick
I - I
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ii :
^ r r r
fi
to
. , 1,
f
h
^
.n^^. Ik^-l-li +
L -
to
r-6~i
.
"
quick
Whose
' P i P f *
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r r r r=
- judge both the quick
V I I I I I J I
Whose
| 1 1
quick, the quick and the
dead: 1 ? 6
have
FOUR-PART WRITING
137
1^ ^
^ -
>^ ^
i 1 k I ^1
whose
King - dom shall have
-' j J ft -r-
nn
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Hft:
' *r i
end
.
^
y -a :
i r I
whose King
_.. i
r i H
dom shall
? ._ tira
&Y\ A TrrVl
' gj ! 1 * 2 m
-jLj L rd
no
end,
./ b if-
-wr
end.
end,
shall have no_
. Write an original piece of counterpoint on the lines of Ex. 195 and
Exercise 23.
Ex. 196. This has only one theme, unless the little counter-subject
first appearing in the alto at bar 3 is counted as a theme. There are
two cadences, one at bars 9 and 10, the other at the end. The first
one does not mark the introduction of new matter, as in Ex. 195, but
of new treatment of old. Here the imitation is one bar closer than
at the beginning. The solitary pair of quavers at bar 11 may have
been inserted to avoid tautophony. The D in the alto at bar 16 is a
minim passing note the only one all the Test being crotchets.
138
COUNTERPOINT AND HARMONY
Be
ne - die - tus
Be
ne - die - tns qni .
ve - nit, qni
r 1 rt i i
m
qni .
m
=i=i
Be
ne - die - tns qni .
I
m
8
-nit, be
ne - die
tns qui
'Be
ne - die - tus
9
FOUR-PART WRITING
10 11
139
r r r
ve - nit, .
be
ne - die -
ve - nit,
be
ne - die - tns qui.
^
HE
ve
nit,
12
13
14
-tus qni - ve - nit,
be - ne
ve
nit, qui
ne - die - tus
ve
nit,
r i 1 r r if
qui.
T6
nit,
nit,
140 COUNTERPOINT AND HARMONY
Fill in the missing- parts, taking Ex. 196 as a model.
Be ne - die - tus qui ve
r r r r
_ qui ve
nit,.
qui ve
-nit,
Be
ne - die -tus qui ve
^E
-nit, be - ne - die - tus qui
nit,.
-nit,
ne - die - tus qui ve
FOUR-PART WRITING
141
be
ne - die - tus - qui ve
=
Be - ne - die - tus qui ve
t
Be ne -
^ o' J J |J J [' " |J
-nit,
i ve
nit,
-nit,
m
-die - tus qui ve
nit,
be
ne - die - tus .
r r i i J 1 IT r
- die
tus qui .
ve
nit,
qui ve
nit, qui ve
nit,
142 COUNTERPOINT AND HARMONY
26,-Write an original piece on the model of Ex. 196 and Exercise 25.
7. Add an Alto and Tenor, not in strict counterpoint. The square brackets are
placed over notes where there is no change of root.
Somersetshire Folk Song, * Gently Johnny my Jingalo*
^ (Copyright)
28. Add Alto and Tenor.
Somersetshire Folk Song, ' Searching for Lambs 1
(Copyright)
Bar 4 has been altered from 4 to ^ time.
p
^
4
p=
^M^
=f=F=f
=^=
__
=N=
^=p
^E
^
^^
=*
^
I J J
p
,
6 t
r-
=t=
-i
J j J
i i *"
__^l 1.
w
r ' r
=M=
<
1 5
^
i=>
,,
,
=^=
*
=P
TH
i
M
^=4=
, Add Alto,Tenor and Bass.
FOUR-PART WRITING
30. Add Alto, Tenor and Bass.
143
f ln dick Karti icK gehoffet, fferr! CalviniuSj (f58f)
al form
rr u ij,i "
L jfr>r ir LJ.IJ j
C7 "v_x I '
31. Add Alto, Tenor and Bass- Supply your own chord? changes.
J NJJ jj ij
J
r r r
32.Add Soprano, Alto and Tenor.
r r ir r
r r ir r ir r r
*>f J' J7
J J
r i r r r
33.Add Soprano, Alto and Tenor. Minim passing notes may he used at the
square hrackets. Chorale
rrif rf'T ir j ^ ir f
144
COUNTERPOINT AND HARMONY
34. Add Soprano, Alto and Tenor. Keep a flow of quaver passing notes mov
ing in one or other of the parts, except at the cadence at bar 3.
N ir prr
35Add three parts to the melodies and basses in Section VII, Examples
151- 154 and Exercises 15- 17.
36. Add an Alto in unbroken 4^ Species, and a tenor in First, beginning
as indicated.
from Andernach Gesanglnch
ft
b
^j
:
e-
1 ~~
- e
i n
#
**
~?
O-
r^
-f f
CL
/
f
"ft"
,Z_
ft
l>
t-n
-0 1
e
o-
e
' &-
vy
^s*
-^ ^<j i
^^
P
4U
"
r^
o
-0
Q
ft
^
r~"
o
*J
*
*
-e
v
^ --
e
-,*?
&
^TT
O i
TQF '
TTf 1
1 4
4
a i
^
E
r
1
f
i 1
a
o 1
-G
TJ r
o
/7\
f
**
! Q
TI
4
11
-e
"*
~^
L
/7\
9^
a 1
r
f
13 1
r
*
"O 1 "
FOUR-PART WRITING
37. Add a Soprano and Tenor, both in First Species.
145
Jz o
o
T
o 1
i
tl 1 -
Tf
TT
o-
"-
A
^=
^^=
=
C.F.
+$4,
JXZj
r?
P ;
n
x-
f f
f,
X
fT
P~
'.p g
L 1
-
L
M
1
J
jf ^
"
^f 1
**
Ti
^s
-&
-o
x
^. s~
-o
-'^^
w
nr-
1^^
=^
LJ 1
LL_jLJ
M 1
^
x-*
=FP=
jj .
-
T
I
T:
i
s~
xr~
x
,x-
-e*
-5^
^
fr
1 ~/*-
|r~ i
Jt C.
P-
W
>J
?
6i
s *^
1
1 J 1
o
38.Add an Alto in First and a Tenor in unbroken Fourth Species.
r-fl-
^
-Q
-i
_ -^
r~
n
1
j-e
"T
rn
-4
a
o
-TTTl
J
C.F.
a--
rr~ "
il
-o-
"TT"
p
u
f.i
-*-
_UL
_ JL
L
it
TT
TT~
4*-
/7\
J
IT"
11
"C
I~
"
ct
--O-
-rr-
^
T"
-n
r
-e~
^i:
? *
-&-
_IJ_
nd
-c
^
7^
JJ_
TT
-*
*-
Tl
r
TT
"o~
1 ti "
146
COUNTERPOINT AND HARMONY
39. Add an Alto and Bass, both in First Species. The Bass imitates
the C.F. for the first few notes of each phrase, beginning one bar
after it, as indicated.
Tf-fe
\ m
'<B
-& n
'^ rt
-a |-
1-F
T '*
* i
~l 1
w-
V
k=
\
-1
rH
TO
1
1
-o
r '
-1
-
,^-
-x
-e
cfa
, p-j-^
I J J '1
n
rfn
f
x-"
x
^^ *
m
rfii
fcz=
r/ "
^^
"
_^
i
j
:-
i- O "'
j i
^ ,
-1
-e
** 9-
,
n
n
-4
i Mn
r\ '"n
r
1,
rk 1
^
-e-
-^.
"-
^.
717^
J
1
NM
1 -
^^
^ P
^
/rs
liiH j
1 P-]
1
fm
rf^rn
N
N.
x^
^ ^^"
Mv^l
v
-s-
r^~Ti
fj>^j j
i 1
-o
M-
n
rH
rH
j-
^
o
"** .
-e
- x ^
^/
'^ b1>
are two chords in this bar
40. Work in four parts, (one in Fourth and the rest in First Species) the
C.Fs. given in Exercises 13 to 18, Section VIII.
SECTION X.
SUSPENSIONS IN XVIth CENTURY COUNTERPOINT.
132. As Gothic architecture developed decoration became more
profuse, and much in the same way the composers of the Polyphonic
Period gradually began to round off the corners, preserve the continuity
of movement, decorate and beautify their work with passing notes
and suspensions, simply or ornamentally resolved.
133. The ornamental resolutions used by Palestrina were of two
kinds, as shown in Exs. 197 -(a) (b) and (c) ; (c) being the same as (),
except that it is in notes twice the length ; (b) does not appear so fre
quently as (c), and both are used sparingly, by far the greater number
of suspensions being resolved simply. Ex. 197 (a) is the earliest example
of the anticipatory note, that is, a note drawn from the chord following,
and repeated when the chord changes. It is always of considerably
shorter length than when it is repeated, for it is natural that the orna
mental note should be of less rhythmic importance than the structural
note. The commonest form of anticipatory note is that shown in
Ex. 197 (d). It does not occur in XVIth century counterpoint.
Ex. 197 (b) and (c) are still further examples of ornaments constructed
from the notes lying next above and below a harmony note (104).
In a string of suspensions plain resolutions are alternated with
ornamental ones to avoid monotony, as in Ex/ 197 and Ex. 198;
(a) was often followed by the rhythmic figure found in (6), but without
the suspension, as in the tenor part of Ex. 199. The quavers need
not necessarily be in the part which has the suspension.
Ex.197
(a) (b) (c)
_ J J J'-'J -Fl r=n
r
j ^ T i
i j J ^
m
~^, j j
-e
148 COUNTERPOINT AND HARMONY
Ex.198 P&lestTinait'Assumjyta est Maria?
*t
do - na no - bis pa
cem.
-bis.
60
pa
cem.
-4MI
-bis pa
Hen
p t i-cein,
do - na no -bis pa
^
cem.
Hefl
no - bis pa
^
cem.
-cem, do
no - bis pa
Ex. 199
Palestrina, Sacrum Convivium?
n
134. The Tudor composers were more progressive and developed a
few more ornamental resolutions. Ex. 200 shows a drop to another
note of the chord between suspension and resolution, whilst Ex. 201
(a), (fc) and (c) all taken from TaUis's " O Lord, give Thy Holy Spirit "
shows the same idea, but with the intermediate harmony note lying
above, instead of below, the suspended note. In Ex. 202 the second
quaver instead of descending returns to the suspended note and then
leaps a third to the note beneath the note of resolution.
Ex, SCO
O. Gibbons
r
SUSPENSIONS IN XVIth CENTURY COUNTERPOINT 149
6)." I . . . .._(). . , (c)
Taliis
*
rff
fT
,
r-
Ex. 202 Byrd. 'Prevent us, lord*
*^
r
r
r
135. The polyphonic composers were more concerned with move
ment than with harmony, and with intervals than with chords. It is
therefore easy to understand how they arrived at the type of suspension
shown in Ex. 203 (a) and (6) (both from Palestrina). At first sight
these examples look like a departure from the rule that only triads
and their first inversions may be used, for if the tenor F in the first
bar of Ex. 203 (a) was an ordinary suspension of the 6th in a first
inversion, there would be no 5th, D, in the chord (122 and 123, and
Ex. 156 (a) ). Likewise at the first beat of the second bar in Ex. 203 (6),
if one of the notes of a triad had been suspended, the bass would have
been F, not E flat : and at the third beat, where the bass F is suspended,
the note in the upper part would have been either B flat, the 5th of the
triad of E flat, or C, the 6th of the first inversion on E flat. The rule was,
however, that any note could be suspended provided that it was pro
perly prepared and resolved, and provided that all the parts not concerned
in the suspension were in consonance with one another. Thus, in Ex. 203 (a),
the soprano, alto and bass form the triad of G minor, and, in
Ex. 203 (fc), second bar, first minim, the uppermost part and the bass
form the consonant interval of a major 6th ; whilst at the third minim,
where the Bass is suspended, the two upper parts form the interval of
a perfect 5th. The difference between this type and other suspensions
is that the chord must change at the moment of resolution, whereas in
the others it may remain unchanged. But it will be seen that this
change of chord is always effected by as much conjunct movement as
possible. The three examples in Ex. 203 (a) and (b) are the typical
resolutions. Even the resolutions given in Ex. 208 (c), where the bass
leaps, is uncommon in XVIth century counterpoint, though it may
be freely used in the exercises with melodies and basses which follow.
Later on it will be found that discords all resolve in one or both of these
ways. Every student will readily recall numerous uses of this type
of suspension. A few very well-known ones are given in Ex. 204.
150
COUNTERPOINT AND HARMONY
Ex.303
.fo)(
Tu es Petrus
^=
6E
' Dies Sanctificatus 1
( * *
H O " H
Ex.204
\ih\ |
* ' A
Vund&e*
^"^ g
*Jlr(f H
f
, T
rr
i
1 6),
'Innsbruck* Hack's Harmony
JkrJJ^J
7 BacHs Harmony
j.j
J.
^
Ex.30
Palestrina, '
*
I
SUSPENSIONS IN XVIth CENTURY COUNTERPOINT 151
A\ Ibid, Sacrum Convivium?
lp*=f=
=Wt
fV=
& r r
^^
136. The second bar of Ex. 205 (a) shows two suspensions, the
first of the type just explained and the second a further type. Here
the suspension of the F in the first soprano is prepared by a note at
the distance of a 4th from the bass, and therefore breaks the rule given
in (122) (preparation). The whole progression from the second bar
to the end is the nucleus of the more modern Dominant Pedal. This
is the dominant of the key lield on in the bass through harmonies of
which it is not a part. The only rules with regard to it are : first,
that it shall be a part of the first and last chords in the progression ;
second, that the next part above the bass shall act as the bass for the
time being. It will be seen that Ex. 205 (a) fulfils these demands
(although probably Palestrina knew nothing of Dominant Pedals),
for the passage is in F major : C is the dominant and is the root of
the triad where the bass commences the " pedal point." The harmony
returns to this triad at the last minim in the bar, after which the bass
quits C for F. The first tenor is the next lowest part. At the second
minim it resolves the suspended B flat on to a first inversion of the triad
of F, and at that point the suspension in the soprano is prepared.
After that the bass part resumes its functions, relegated for a time to
the first tenor. In Ex. 205 (b) the A flat in the second tenor is one of
the type of suspension already explained. When the alto prepares
the next suspension on the last minim in the bar, the second tenor is
the bass for the time being and makes the chord a first inversion on G.
152
COUNTERPOINT AND HARMONY
This type of suspension should generally be employed at an important
cadence, and approached and quitted whilst the bass holds the fifth
above or fourth below the final bass note of the cadence. Ex. 205 (c)
shows it in its simplest form in four parts.
137. Ex. 206 (a) has two double suspensions in it, one on the third
minim in bar 1, and the other on the first minim in bar 2. In order
to make this clear, the passage has been rewritten in Ex. 206 (b) leaving
out the suspensions. Ex. 207 gives another double suspension in three
parts. Double suspensions need no comment and may be freely used
by the student. When the root and fifth of a triad are suspended
together there will of course be either consecutive fifths or fourths.
The fifths would be wrong and the fourths are somewhat bare and
crude. To avoid these one of the parts must have an ornamental
resolution, as in the first soprano of Ex. 206 (a), bar 2, 1st minim.
Ex.206
Palestrina, Kyrie to 'Assunipta?
*_
T= ^
= 5f= ir=
=n=
*
u
TT
u o
Ex. 207
Ibid
188. There remains one more type of suspension to comment on,
the second resolving on the unison, as in Ex. 206 (a), first soprano
and alto, bar 2 ; and Ex. 198, alto and first soprano, bar 2. In (124)
this suspension was condemned, but Palestrina uses it freely. He
makes the part progression, however, much clearer by the use of an
ornamental resolution. The reiteration of the F in the soprano of
Ex. 206 (a), and of the G in the alto in Ex. 108, make it quite obvious
that those parts are dropping one step, whereas in Ex. 161 (i), this is
not the case.
SUSPENSIONS IN XVIth CENTURY COUNTERPOINT 153
139. A suspension gives added weight to an accent, and if the
law of agogic accent given in (114) has been understood, and care is
taken to abide by the rules given in (122), there should not be much
doubt as to where to introduce suspensions. The occurrence of a
long note beginning on an unaccented part of the bar and followed
by a drop of one step, is a sure sign that one is necessary. Ex. 208
(a) and (b) shows the effect of such a note without and with a suspension.
If the long note begins on a strong accent, the suspension can still be
employed to give more stress to it, but it will be in another part.
Ex.208 . a)
I ' *
Ff=F
J j
*/ -f!
1
^=
9*
f=
^
i.
9
i
I
i
9-
i
i
e-
n
i.
i
n v
|Jj.. J |
4s&
J f
r r r f
o \
fl ^* IP
T r j ^ *
-e
L*_
ir f r ' '
Ex. 209 shows the effect of such a note (a) without a suspension, (b)
with one, (c) with a very strong double suspension. Par. 122 makes it
clear that in triple time a suspension cannot be prepared on the second
beat, struck on the third, and resolved on the first of the next bar.
In XVIth century counterpoint it is either prepared on the third,
struck on the first and resolved on the second" beat, or prepared on the
first, struck on the second and resolved on the third. This seems to
contradict (122). But where long notes occur on the second and third
beats of triple time, the agogic accent is stronger than the bar accent.
Therefore such progressions as are shown in Ex. 210 are satisfactory*
Ex. 309
I* f 1
1 c
*
ft;
I J J *
J i
f
\
JO.'
\
.
-CL*
UL^J
F
L_u 1
1 0= 1
k
'[' f "
1 ^-e^ U
(c)
Ex. 310
154
COUNTERPOINT AND HARMONY
Exercises on Section X.
In the first eight exercises use the ornamental resolutions of
Palestrina only. In the first four the places for suspensions are marked
with asterisks placed above when the suspension is in the upper, and
below when it is in the lower part.
1. Add an Alto beginning as indicated.
3HE
2. Add a Soprano.
8. Add a Tenor.
4. Add a Tenor.
r ir rr
r rrrr rr
1* r r r
SUSPENSIONS IN XVIth CENTURY COUNTERPOINT 155
5. Complete the following by adding parts where there are no rests.
M
6. Complete the following for two Sopranos.
ft*
f*
^ 1
~T f J J j J
h
*-& j-^
_
-** o
7. Complete for Alto and Tenor.
fe
156 COUNTERPOINT AND HARMONY
8. Complete for Tenor and Bass .
=wt=
9. In N9? 9 to IS use the additional ornamental resolutions of the Tudor composers.
Complete for Tenor and Bass.
-or
MI 1 P I
ffl
r^
rpi
I o 1
ti I
noii
im rr
fU
LL.J
I 1
10. Complete the following.
i
SUSPENSIONS IN XVIth CENTURY COUNTERPOINT 157
Ex, 211
Thomas Morley (1557-1603)
Go ye my can - zo - nets to my dear dar -
Go ye my can - zo - nets to my dear
-ling, go ye my can-zo-nets to my dear dar -
qr ir rr
dar -
- ling, dear dar - ling, go yemycan-zo-
-ling,
go ye mycan-zo - nets to my dear dar - ling, to
-nets to my dear dar -
ling, to my dear
Ill, r , J -
r-j
i
__ p 1
9> r r fj -^
my dear dar -
"'^
- ling ,And
^^
: 1 ,
with your gen -
1 r i
- tie
1
, V^T p
~-^N
1_
N
g K
* *
i J J
1
dar
ling, And with your gen -
r cr r
J r r ^
dain - ty sweet ac - cent - ings, Pe- sire her to vouch-safe these my la-
-tle dain- ty s weetac- cent - ing-s,De- sire her to vouch-safe these
158
COUNTERPOINT AND HARMONY
^^
r r
-ment - - ings, de - sire her to vouch- safe these my la-
my la-meat - ings, de-sire her to vouch-safe these my la - ment -
tr^
C.
^
*
==
-
[^ j 1-^~^^ U,
I
- ment
ings. And with a crown-et of her rays
^ j
r p
1 |_J
1
-$B J a
1 5!
| " H= ^
1
ings.
And with a crown - et
r r" ' i r * rTr r r r ir V r r
su - per - nal, T'a - dorn your locks and make your name
ir r
of her rays su-per - nal, TVdornyour locks and make your
1
e - ter -
- nal, t'a- dorn your locks and make your name e-
name e - ter -
- nal, t'a- dorn your locks and
make your name e
nal.
SUSPENSIONS IN XVIth CENTURY COUNTERPOINT 159
11. Complete the following on the lines of Ex.211
Go ye my can - zo - nets to my dear dar
ling,
m
Go ye my can - zo - nets
go ye my can-zo-nets to my (tear dar -
go ye my can -zo-
Go ye my
fin
.1 i
- nets to my dear dar -
- ling, to my dear
And with your gen -
j MI j
dar- ling .
And with your gen - tie dain - ty
sweet ac-cent-ingSj De - sire her to vouch -safe these my la-ment - -
160 COUNTERPOINT AND HARMONY
de - sire her
-ings, de-sire her to vouch- safe these^ my la - ment -
1
And with a crown - et of her rays su -
-ings.
And with
per - - nal,T'a-dorn__ your locks and make your name e -
Ta - dorn your locks
-ter - - - nal, t'a- dorn your locks and make your name e -
ta - dorn your locks and
- ter - nal, and make your name .
e - ter - nal.
SUSPENSIONS IN XVIth CENTURY COUNTERPOINT 161
Ex.313
SOP.I.
Q/
/v
2nd time Sop.n.
' i J 1'-= I i p""
Thomas Morley
fln *<* J 1* [I
Mi - ra - cu-lous
Sop.H.
f J !*- j-j : h-*1 1 1
love's wound-ing, love's wound -ing, mi-
2nd time Sop.I.
HP ii- i r> 1^ PI
TO ^ * J p^~
Mi - ra-
-f+ IM ' : ^ 4 P
cu-lous love's___ wound - ing,
^^== =3=*- 3=)=^^
-ra - cu-lous love's ^
iv-i =T=3f==
g ^_ ff i^ j
vonnd - ing, mi-ra - cu-
-1 \ ' r
M r i i
lous love's wound -
ft, t -^ggr^,
i <* =$= * r
J ,L W
mi-ra - cu-lous love's wound - ing, mi - ra - cu-lous love's
- ing. Mi- ra*culous\A -ing. E'en those
wound
- ing. Mi-ra- cu-lous love's -ing. E'en those
4 I I
darts my sweet Phil-lis, Een those dartsmysweet Phil-lis,So
dartsmysweet Phil-lis, Ben those dartsmysweet Phil-lis, So
1 "r r 11
fierce-ly shot against my hoart re - - bound-ing, re - bound -
Jjjijr
fierce-ly shot against my heart re- bound-ing, re -bound - ing, re - bound
M
162
COUNTERPOINT AND HARMONY
f^^^^fe^fe
- ing,Areturn'd to Ros
Ltjr* J ' J J 1- i r ^rw^
J |H
- es, Vi - <
1. 1 r r r i
- lets and Li - -
f-p f-
(m * A * - ~f * (- P
- ing, Are turn'd
n f e
to Ros - es,
ffrT^ -!
M 1 h-
Vi - o.
r j j\\
.|i L^! p p_ l_j
- lies, Vi - o - lets and 1
bi . i j. KI nj j =F
' djd frrr -+
,i - - - lie
i r r i r
r J - |L -
s,With o - dour
p
fe " r j v " j* 1 * ^ =1
r- 1 1 1 1
P^ 1 1
-lets and Li - - lies, Vi - o - lets and Li -
sweet a - - bound-ing, sweet a - bound - ing,
-lies, With o - dour sweet a - - bound - ing,Witho - dour
With o - dour sweet a - bound -
ten
r? ^
rrr
sweet a .
bound-
I-JJ | t J
dHt
ing. Mi - ra-cu-lousV The last .
two burs are
\asfollow$:~
ing.
1 r 1 1 Mi 1
-ing, Mi-ra - cu-lous love's
ing.
SUSPENSIONS IN XVIth CENTURY COUNTERPOINT 163
5. Complete the following on the lines of Ex. 212.
Mi - ra - cu-lons
love'swound
ing
-ra - cn-lous loves wound - ing, mi-ra - cu-louslove's wound-
mi - ra- cu-lons
ifc
:z: ^-^ ~~~""" -^ \fstiime .
\\ 2nd time
8-H -)
W 1
oj
t
r . Cf [1
ing, mi-
ra-cu-lous"
^
-si- 4 J
4 J
- ingjlenthose
-- hH- j 1 J
|J K h i
^_
%)
d?~E d h F i
|4 1 4 f * w - ^- ' ^ ' J h4-
Een those_ dartsmysweet
15 , , ^ ^.
A
i* ^ J '* i
Phil-lis So fierce-lyshot against my heart re - "bound
164
COUNTERPOINT AND HARMONY
I
P
-ing,re - "bound
ingjAreturndto Bos - es, Vi - o -
-lets
Vi - o - lets and Lil - ies, Vi - o - lets,Vi - o -
With o-dours
-lets
With o-donrs sweet a- "bound
i
with o-dours sweet, with o-dourssweeta -
\J
ing. Mi - ra - cu-lous\/ $*l Segno
Thelastlar willle
a IrevepsinMorley.
Mi-ra - cn-lous
SUSPENSIONS IN XVIth CENTURY COUNTERPOINT 165
Exercises 13-15 should have Palestrina's resolutions only.
13. Add an Alto, commencing as indicated.
Sop. and Alto
14. Complete the following.
r
- -"-
-^
L=l
^
-tf=
*r
^ . =
-
-
r;
^
^i
o o -
if
^ ,.
>fcr ** **
o
1
b rrrrf
rrrrr
^=
f^
^H
^ i r i ' * ^
j
166 COUNTERPOINT AND HARMONY
15 Add Soprano and Alto accordingto the figuring.
ft
k t* 1
it
65 96
1 76
r "
6 76
o *^
766-
3--31
76 4^8- 6558 46 '# '656 $ 34564#3l^3 ft
16. Add a 2nd Soprano, which may cross the first freely. The next three exercises
are in the English style.
pga
p y,*j
S
17. Add Soprano and Alto,heginningas indicated.
^
-.>!>[ 1 F---F
^
--
Ml :
18 . Add Soprano and Tenor according to the figuring.
I
7 6 a 6 73 6 6 5
- 4 ft
4);. r ^ rr
^x""""^
? Jf"
p-o- ,
^
y^ i& ti
3^ 1 M 1
f 9
2 6 6 65
6 1)6 4 6
3 1>3^
~~*)*T
j5>
-o
j.
r m
-O
^ 2
^7 H
-*-* i
*
43
5r,
566
/t
^ H
4
H 0_. _
K *
SUSPENSIONS IN XVIth CENTURY COUNTERPOINT 16 r
Fy 21 S
r, A. /c/it) From the genedfctus O f p a iestrina's MissaBrevis
\\A. \> \ Ml 1
-e n
f-
f f
^ Be -
ne - die -
r^ h
tus qui ve
H
BD
US 3
Be
ne - die -
u 1
yr i A 1
j*~^*^
* " rj e -r t J "
nit
(
in
L. ......
......... ... ve -
839-, z f | 1 f 1 1 F- f P ^
^
0-
_|E_B_4J6 m -
^fc==l I ' 1 ll 1 1 I
- tus qni ve -
|^-|> 1
DQ||
-
H
* & 1
Be
1
ne - die -
fluir
>.Jj
1R 1
Vp-
BitC
r r *
-p i
-
_^ &
___
e
nit,
r f
>ff
9
Be
r^
r ^ r
-
ft
| HCJll
nit,
>
q
ro
L ni .
re
^
*~
>r ^
s :
ins aui ^
ye
j;
n
it, uu
i .
1 i
rf 1, mi
-n
p M j'r^ ^ -j
^-2
ne
P f 9 1
die - tns
qui ve
If
nit,
- P rrfn
qui ve
N
ve
-'- ULJ-
nit, qni ve
1 1 II \XL
nit
OL J
=
5T-
1 1 j j | STF ?T~r i
fi^t-J I-M
-
nit
=="
=t==i
no -mi - i
ie _ ......
- } - nit
1 1
in
f f r if F P
JID
H 1
"r n
_j-J H 1 1 L_
in no-mi - ne.......... .......-.................. Do -
L68 COUNTERPOINT AND HARMONY
J L ?- a G ~n 7i 0*-. ar-h= =
flj^-l h F
*> Do-mi-
1 1 If " Q s .*>
ni, Do - mi-ni, in
no-mi- ne
. m no - mi -
= n= 5 rsff rl =1
L L_ 1 _t
o f. J-^-^f-
mi - ni,
in no - mi - ne.
Mjj rr r r ]
Tr~P i*r -'^i
m-j: ^
no -mi - ne
in no -mi -
-. J** pr r 1
ne
f--l 4 p
L L J r =\
r r i
Jg,J> e ei
-ne Do-mi -
jd,
1 1
in no-mi -
ne, in
T 71 ^ T^ r
[1. ' . I 1 1 1 ' ' 1
\ .... 1 1
i h-p --P r r r '
H
Do
ff P i ^- r
^ 5-
*=
Do - mi -
p j J pr 1
ni, Do - mi-ni, in
r r r r r r r^if r r =\
no -
mi - ne,
1 1 1 1 ! ! 1
-III
I* r_e=t
jia
/J r.
1
mi - ni,
in no - mi -
Do -
in no - mi - ne.
-ne Do
mi - ni,
in
mi - ni.
Do
mi -
no-mi-ne.
Do - mi
ni.
SUSPENSIONS IN XVIth CENTURY COUNTERPOINT 169
. Complete the following, using the excerpt from Palestrina's Mass as a
model-, the last few bars should be original work.
f_ 1
n i j j J (> i
r^-f-o 7, i
itT 2 MI
O tl
r j *
-AJ
IP
|Htl j
W
T
- JJ mr*f~
p* *\
__^J^
fe
. .
jj rr r
= r
- jJ r r(H
x.
li 1 "I 'M
rrf rf
1=
i
B %j rj
. F
1 1 !
&
y 1 .1 ^ ^ p~
4M
t=J
-
=
^==H
^.
v
p
iff- rr
PS
^
i
F
M
170
COUNTERPOINT AND HARMONY
Ex. 214
From the Agnus Dei of Byrd's Mass for Three voices
2^9
pa
cem, pa -
pa - cem.
The analysis of Ex. 214 is as follows :
Bar 1. Theme in Alto, ihiitated at the 5th below one semibreve
later by the Tenor, and at bar 3 by the Bass. The first four
notes of this theme do not appear again, but the rest of it
will be found in the Alto (bar 4), Tenor (bar 4), Bass (bar 6),
Alto (bar 7) and Tenor (bar 8). Most of the ornamental
resolutions of suspensions alluded to in Section X are to
be found in it.
20, Write an example of 3 part counterpoint f onnded on the excerpt from Byrds
Mass. Invent the themes, or else use those given "below.
SUSPENSIONS IN XVIth CENTURY COUNTERPOINT 171
IIP! jy
SJ
ff 1
^_
_KL t*_
Rlh
-I 1 - 1
j
'i i i
-i p
'* \>\> PH
1
The first three exercises should have Palestrina's resolutions only.
1. Add a Tenor part
. Add Alto and Tenor. Put suspensions in the middle part sat the places indi-
-catedhy the asterisks.
I .L> jr . 1
_0
1H
"*v> L
O j> t * " " [
^ L l> J^ HolT "
-e- |0
I
O i%
172
COUNTERPOINT AND HARMONY
23. Add Soprano, Alto and Tenor. Only the suspensions are figured. Passing-
notes and ornamental resolutions must be added.
==
5 6
2 a
7 6
5 3
-Hn-J a o
-5
=3=
| IMI |
IW H
^LJ^ I_
4
M
7 6
9876
7 6
L^
6 5
4 h
N
Supply the missing parts.
&
f'T
f
DOC
j^ J !
g.] |j|
H rJ- |g<
IIM
f 7 "
[ ^-
V
. (a) Transpose the melody of the following tune a 4th lower. Put it in the
Alto, and add Soprano, Tenor and Bass.
(b) Write it for Tenor in the original Key and add Soprano, Alto and Bass.
3" 0. Gibbons
(c) Add Soprano, Alto and Tenor. A few figures are given.
7 6
SUSPENSIONS IN XVIth CENTURY COUNTERPOINT 178
Ex. 15
From the Cruoifixus of Palestrina's Mas$,'Tu es Petrus'
t\0 i b a ! 1 pi o 1
ihd i f ' '
^ Cru - ci - fix - us e - ti - am" p
l^'ftH | - lr J IT^
-' J J r
ro no
^ ALTO ^ ru - c * - fix " us e - ti - am pro no -_^
tlT) i ' iL Ml t)-O ** *-* j g r =
Cru - ci - fix - us e - ti - am,
jirfc TjENOR
i rr i J i
A Cru - ci - fix - us e - ti - am pro no
./A 5 6 , 7 8
JL_b e n x HI " m ~~
4-^> 1 i r i i
** -bis, e-ti - am pro-no -
IIP \\> * p 73 == p:
bis
IlifC l> f r O O
iiJ 1 1 1 1
- ti - am pro no - bis
IIP^J^ZiL^g..-.^ [lip ^f
: l_f . HH
Sub Pon-ti - o Pi -la -
_p L. .,,., ^r, j^
_L __ J ._ m f K
r r r r -J l
i$ i 9 10
^-j - ^-^^ rr r
bis Sub Pon-ti- o Pi-la -
11 12
4 ^ f
^ Sub Pon-ti-o Pi -
Jf L'' = JH I
la -
1 1
-2 = . * J
** ,Sn]) Pon ti
o Pi -la -
-_ -_^ - to, Sub
Pon-ti - o
J Pi - la -
^ to
v. 13 ] 14 15
16
--n p ]
.gL_k o g o o :
** -to pas -sus, et se
--& o P=j^= r
pul - tus
J f
est. . Et
b- 2 f l^f p u e
^ -to pas - sus, et se - pul - tus
est. Et
- to pas - sus, et se - pul
tus
ffl"* F~~f P~"
est. Et
^ pas - sus, et se
f r r r
pul - tus
- est
174 COUNTERPOINT AND HARMONY
17 , ,18 19 20
re - surrex-it ter-ti - a di
Se -
re -surrex-it ter - ti-a di
m
re-surrex-it ter-ti - a di
Et re - sur-rex - it ter -ti - a di
22 23 24
ry-r
7
[ p
m m f m rj . p
- g o ^^fc h^. ^ *
^
-Cl
in-dums:
cri
r r'r r
ptu
--R I r r u
ras, se-cun-dum
J
Se - cun-dum scrip -
tu
v o
- r ' : r
,
i*
e
1 111-
Se - cun-dumscriptu
i . i. _ f i
ras, se - cun-
IBD j e
L
25
26
27
Se - cun - dnm scrip-
28
^P
-scriptu - ras.Bt as-cen-ditin coe
- dumseriptu - ras. Bt
Se - det ad dex-teram Pa
as-cen-dit in coe
lum,
SUSPENSIONS IN XVIth CENTURY COUNTERPOINT 175
33 34 15 36
tf
"-
^ . P P~P P"
i^r
TN
=F
3*
F
r If ':-J=j=q
dex - teram Pa
4, .
p
-gULf
-j
rJ 1^
-
-P-* ^-T*
If
jh
j,,
ri
tris,
se - d
et ad
= 1
dex - te-ram
^Tr~ rn
tf==3
_
^/^^^TT^.
r i r r j '
v<
f
^
|_J L-]_
> ' .' '.
i '
iT
-
P [
tri&
s*
-'^
rrrTf '^> p . i
111
A
Se
- det
a
d c
E EE
Lex-te-ra
=t
m.
nz
i
p a . -
rfjM 8 / j j
4-
6
3U
40
v -tris. Et i - te-rum ven-tu-rus
_u
est
Cl
w
am
glo - 1
i-
^ ;
u -
4=
Pa - tris.
mt^ = r r ~ 2
Et
i
P
- te-rum ven-tu-r
P 1^ it f
us
est
d
cum
P r^ P^l
|^ 1 1 1
Et i - te-ru
IrV* f 3 f 3 J '
m v
^
en-ti
i-ru
1
s
f r
est
a
cu
im
glo - i
pi * I
i-a j
u
u-
-
JU
~^n
- tris. Et i - te-rnm ven-tu-rus est cam glo- ri-a jn-
41 42 43
yy-j
--5 ,
^_j
-_j 1 j
- di -ca-re
JL, \s 9-*- 09 1
^=\
vi
.
vos et
mor - tu
- OS.
J.
pr f
glo .
ri-a ju
- di-ca -
re vi -
vos et mor-tu - os.
if J r rl o^
- di
IID t
- ca -
re
1
vi
vos
-** -o
1 - J ^^r=JI
et mor-tu - os.
JIU ^rJ fl a
H
- di-ca - re vi - vos et mor - tu - os.
Note the small compass of the voices and the smoothness and
variety of their motion. There are three leaps of a 5th in each of the two
higher, and five in the two lower parts, no leaps of a 6th, and one leap^
of an 8th in the Alto and Tenor. Analyse the suspensions at bars 6,
13 to 15, 20 to 26, 29 and 43.
176
COUNTERPOINT AND HARMONY
#6. Write a movement on the lines of Ex. 215. The following may be taken
as a guide. The rests need not be strictly adhered to, but the last note
before a rest should be a long one on a strong beat. There should be a
rest before any part makes an entry with a point of imitation.
Cru - ei - fix - us e - ti - am pro no
e -
i
- ti-am pro no
bis
n^ i j j J. 'if r rrrM
Sub Pon-ti -o Pi -la - -
i j ib f i f j p f r r f
Sub Pon - ti - o Pi - la -
JL-i i , | 1
lJ j ^TTIi
.M "1 |
-$P 1 J *U J-
Sub Pon - ti -
tf r f ^-
o Pi-la
,
Bfi ^ ^Tj ^ r^ 1
1
-ill) .. *L ?._ .] J
1
- to
SUSPENSIONS IN XVIth CENTURY COUNTERPOINT 177
r 6 o s*"^
"fthP ^
ft o J
d3=
i i i i
^ Pas - sus,
-1 ^
et se
""^ pul - tus
est.
1 - J |
4-t f=
TFT^
J_
Et
9 8
ItDib 4 3
I 1
76 5
fe-_6 - I)
^ Pas - sus,
4s r r SB j
pul
i i i
tus
est.
[Jf\
p
w-*
^
-\
S e
^
*>.
"^
^T
j 1
W-k ""Til '1 f
re-sur-rex -it ter-ti-j
i
di
-
i
'
LJL^J
-
* <> 1
e
P!> . =F
-
TT" ffl
A
Ifl
Z_-
H
t
- " r r -^-i-
Et re-sur-rex-it ter-ti -
a di
*
=|
fc
' 1
cun-dum scrip-tu -
-, O n -^ ft-
=1
1
-Bf
^
Se -
en
n-<
r i . ;
ium scriptu -
^-
4=q
-Hi
f
^
Se
-
Cl
an-c
lum scrip tu
i
y
s~~
-O r.. J
X
-y *^
Ji*
Se - cun-dum scrip-
-A,
-].
__ Q . L
-f - =
Et as -
cen- dit in
\ i 1
coe
t
FT e 1
- ras
1 ** 1
_ Et
as - cen- dit
in coe
S - tu
ras.
Et as-
N
178
COUNTERPOINT AND HARMONY
i
m
se - det ad dex-te-ram
se - det ad dex - te -
- cen-dit in coe
lumi
se-det ad
dex - te-ram Pa
Frt
i p = - * h9
/ & _
r r r ^-H 1 -
-tris.Et i - te-rumv
r f
an-tu-rns
est
J
_, . (._
TT-. p
'
> x, _
*-=f=,=V=\
' 1
B
-? 1
1 F-
t i - te-r
um ven-tu
-+* J-^ )
rus est cum
IPO-! _ j r/ j r/ j
-6>
L_o 2 [ 1
Bt i - te - rum ven-tu - rus est cum
r Jf i ft __|
L
**
n=q
II
In g
r^
Lo -ri-a
ju-di-<
sa-3
fe
feq
^r, r,
H
JK) = =^_*-
hH-
__^ .
glo -ri-a
vi - vos et mor - tu - os:
SUSPENSIONS IN XVIth CENTURY COUNTERPOINT 179
Anthem, by Tallis, f O Lord 3 give Thy Holy Spirit'.
2 3,
Lord,give thy Ho - lySpiritin - to our_
Lord, give thy Ho-lySpirit in - to our
Lord, give thy Ho-ly Spirit
Lord,giv^ thy Ho-ly Spirit:
in - to our
in - to our
hearts, and light- en our un - der - stand - ing, that
IIP 1 t? v
2
hearts, a
nd
-
li
1 1
ght-en our
un-der -
stand - ii
==
ig, that
r.f r .rr
hearts, and lighten our un-der-stand - ing, our un-der-stand -
i' mi I - J J J J
hearts,
and light-en our un-der-stand -
we may dwell in the fear of thy Nam
we may dwell in the fear of thy Name,
^ *. J | V J J J J | '? p =S=
in the fear
-ing, that we may dwell in the fear of thy.
-EiEEEEfe
dwell in the fear of thy
j * iU . ^_ < _^ 11
^ S_4.T_ f -* xl VT
-ing, that we may
10
in the fear of thy.
Name.
J
r r . r r r
of thy Name, in the fear of thy Name, all the days
- JJ
r r r r
Name,
in the fear of thy Name,
in the
a J
Name, in the fear of thy Name, in the fear of thy
180 COUNTERPOINT AND HARMONY
12
/j. IT J J 1
IP -UgU?! 3d
J^ the days of our
liH-frp p r
life,
I 7 1
2
77 fc
ill t
ne
r r i
4t&^ In*
of our life,
a
11 the <3
^ f
Lays
TS>
c
-1
f our li
i 1 _
fe, all the
fear of thy Name,
..y*i (7 o = *
a
-*-f i
1 1
11 the days
-
c
-
)f 01
ir IT
fe, a]
Ithe
1
si J
1 o *
^ Name,
15
all the days of our life, all the
16 .. 17
-i 5 U
days of our
life: that we may know
n == n n rr
U M
thee the
r
days of our __
life: that
we maj
r know
days of our
life: that
we may know
^ days of our
r'fl 18 , 19
life: that
20
= 5
we may know
1 --
_
&- z J " f o
on-ly true God
"R""^ c r v r 5^^*"
r ** (rf -" 6^ jfr-
, and Je-sus Christ whom thoa hast
fr
-^
thee the on-ly true
God, and Je-sus Chi
j [ -=3
i&twhomt
n
hou hast
r 3 s
_g_
thee the on-]
fc): I, i i . . I a :
ytrue God, and Je-sus
o = |S^ ^ ^
Christ \vho:
01
4-
L-^ J J J J 1 f-o"
_9 i ^2
-4-
thee the on-ly true God, and Je-sus Christwhomthou hast
21 22
sent, and Je -sus Christ whom thou has
sent, and Je
sus Christ whom thou hast
thou hast sent.
and Jesus Christwhom thou hast
sent.
and
Je - sus Christwhomthou hast
SUSPENSIONS IN XVIth CENTURY COUNTERPOINT 181
23 24 25
sent, and Je-sus Christ whom thou
hast sent.
sent, and Je-sus Christ
whom thou
hast sent'.
sent, and Je-sus Christ whom thou hast
sent.
This example has not been quoted for its contrapuntal ingenuity,
but for the unusual beauty of its suspensions. At bar 3 a 7-6suspen-
sion, resolved by proceeding to the next harmony note above and then
dropping to the usual note, is combined with a string of passing-notes,
the third of which is accented. At the 1st minim in bar 5 there is
an apparent J 9 but the ear carries on the bass of the previous bar.
At bar 8 the resolution is made by dropping to a note (B[?) which does
not belong to the chord, but is consonant with it. At bar 9 there is
an instance of the natural and flattened form of the same note sounding
together. This need not at present be emulated by the student. It
was not uncommon in the XVIth century. At bar 15 there are con
secutive 5ths between Soprano and Alto and consecutive Tths between
Soprano and Tenor. The second and third crotchets in Alto and Tenor
are passing-notes, and therefore do not affect the situation nearly so
strongly. At bar 22, fifth minim, a 7th is followed by a 9th in Soprano
and Tenor. The final cadence is suprisingly lovely. It is a development
of the suspensions described in (134-136). It is also an anticipation of
the inverted pedal. The part writing is rather poor, there being many
repeated notes and the bass going continually from D to G. These
points and the consecutives are not meant to be copied.
27. Write an Anthem on the lines of Ex. 216. Use original themes or fill out
the skeleton given below.
Ho - ly Spir - it in -
- " | i . 1 1 r 1 1 |i
Lord,give thy Ho-ly Spir - it in-to
hearts
182
COUNTERPOINT AND HARMONY
*-=- f k *
(4S .. p . i f
and light-
=t=
en our
*" r r r
light -en our
... /. ..-
that we may
p
r ... f f ;
and light -en our un- der- stand -ing, that
LJt ", 1
-p __
ft
* f =
that we may<
L ' =|
= f
ti ^ that we may<
r r r rj =
Iwell in the fear
F-f
in the fear
* f r
dwell in the fear
* \ 1 p
p p
we may dwell in the fear
in the
ftS * *TT
i *-^
, -r-i
of thy Name, in the
fear <
:>f thy Name
all
=-^
the days
,^~
>r
9
1 L f
' f r j
r f
1
all
^J i
the days
of
-f f f i
r r r
=M=
4- F-4
fear of thy Name,of thy Name, in the fear of thy Name all_
of our
All the days of- our life ;
All,
-the
m
All the
..the days
that
SUSPENSIONS IN XVIth CENTURY COUNTERPOINT 183
n pj
i J i ..
-ffp
*-
-*-
1
t
lie on-ly
tine God
and
r f
^
*-
y
and Je - sus
-MS
^
that!
we may know
=aF
_.
P
And Je-sus
t 1
9
1 : i i
re may know thee
,the on-
Ly true God, a
nd
Je-suB Chiist,"Whom
t j JP 1
. 1 ? H
Je - sus
f*
. r
r ri T
and Je - sus
4B
i 1
and
-M; p ^ n
and
i r ? r
f ;. , J J-
thou hast
-" ~~
sent, and
Je - sus Christ,whon]
^ r j * =
thou hast,sent and
Christ.whom thou hast
i
Je - sus Christ, whom thou hast sent, whom thou hast sent.
SECTION XL
THE MODES.
140. A working knowledge of the modes and their use in the
XVIth century is essential to the student, and counterpoint of this
period cannot be intelligently worked without it ; it leads to a full
understanding and use of the triad, and helps to free the student's
harmony from the tyranny of the dominant discord. Moreover, a
knowledge of the modal harmony of the polyphonic period elucidates
much in modern harmony and counterpoint that would otherwise be
inexplicable.
Ex.217 The Ecclesiastical Modes,
Authentic.
I. Dorian
F M D
Plagal.
II. Hypo dorian
F P M
III. Phrygian
IV. Hypophjygian
Jf F
M D
VII. Mizolydian
P M D
VIII. Hypomixolydian
M P M
IX. AEolian
P M
X. Hypoaeolian
P F
M
XI. Ionian
P
M
P
XII. Hyp o ion i an
M P
F=Final; M=Mediant ; D==Dominant.
The Locrian and Hypolocrian modes, commencing on B and F,
were included by the theorists. They were never used because of the
augmented 4th and diminished 5th between 1st, 5th and 8th notes.
THE MODES 185
141. The Ecclesiastical Modes, with which we are alone concerned,
are given in Ex. 217. They bear Grecian names and were thought to
correspond to the modes of ancient Greece. Since the method of
Grecian notation has been investigated, however, it has been discovered
that the Grecian modes having the same names began on quite different
notes. Many people nowadays refer to the modes by number only.
These numbers will be found in Roman figures in Ex. 217. Despite
the fact that they are wrongly named, to refer to them by a bald numeral
seems to divest them of all character and romance. Who could speak
of Bach's great Dorian Toccata and Fugue as " The Toccata and Fugue
in Mode II " ? The finals, mediants and dominants of the modes
(marked F, M, D, in Ex. 217) had no harmonic significance. They
got their names through their positions of importance in plainsong, for
instance, the dominant was the reciting note of the Gregorian chants
(Ex. 218).
Ex. 318
F tf D
come, let us sing unto the Lord:
D
i
Let us heartily rejoice in the strength of our Sal-va - tion.
142. Each mode had two forms, authentic and plagal, The plagal
modes did not differ in essential character from the authentic, but
they differed in compass and in one other way. The authentic mode
was regarded as a series of five notes (a pentachord) with a series of
four notes *(a tetrachord) superimposed upon it, .the last note of the
pentachord (usually the dominant) being the first of the tetrachord
(Ex. 219 (a) ). The plagal mode was regarded as a tetrachord with
a pentachord above it (Ex. 219 (b) ). A melody, the compass of
which lay for the most part between the octave bounded by the two
finals of any mode, was said to be in the authentic form of that mode.
If its compass lay between dominant and dominant, it was said to be
in the plagal form. Thus, Ex, 221 (a) is in the authentic form of the
Dorian mode, whilst Ex. 221 (b) is in the plagal form, or the Hypodorian
mode. Actually in Palestrina one set of modes was used for the high
voices and the other for the low. Thus, if a tenor or treble entered
with a theme in an authentic mode, the imitation of that theme in
alto or bass would be in the plagal form of the same mode. It is
from this convention and from the division of -the octave into pentachord
and tetrachord that we have derived the fugal rule that if a subject
commences with either tonic or dominant on well-marked accents, then
the " answer " must reverse the position of those notes (Ex. 220).
186
Ex. 2 19 (a)
Authentic
COUNTERPOINT AND HARMONY
Ex.219 (W
Plagal
Pentachord
Ex. 330
Subject
Tetrachord
Tetracliord
Answer
Pentachord
Ex.
(a)
Ex. 221
Si
143. All melodies ended on the final of the mode. To find the mode
of concerted music, first look at the final triad. Its bass note is the
final of the mode. The form of it authentic or plagal is determined
by the compass of the tenor part, for originally the tenor was always
allotted the canto fermo.
144. The compass of each part was at first restricted to the octave
between the finals or dominants of the mode in which it was written,
but even in the XVIth century composers demanded more freedom
than was allowed them by contemporary theorists. It is, however,
unusual to find a voice part in Palestrina which exceeds the compass of
a 10th, that is, one note above and one below the original octave
permitted.
Any arbitrary restrictions of this kind only cramp the student.
In the exercises which follow it is therefore unnecessary to trouble
about authentic and plagal, as long as the compass of the voices is
kept to about the interval of a 10th.
145. Whilst music was purely melodic the modal system was easy
enough, but with the dawn of harmony difficulties arose. For even
with the primitive method of accompanying a tune by a succession
of consecutive 4ths and 5ths, the augmented 4th and diminished 5th
abhorrent to mediaeval ears had to be avoided. F sharp and B flat
then appeared on the scene (Musica Ficta). The sharp sign was
originally the letter F and the flat sign a b. These accidentals
were rarely found in the plainsonw or canto fermo, but in the
accompanying parts they were used to avoid the ugly intervals
both melodically and harmonically. There was another factor
which led to the increase in the number of accidentals, namely, the
cadence. The charm of a cadence has been potent throughout the
history of concerted music. The perfect cadence originated in the
natural series of Harmonics (Ex. 12), and is indeed, natural to music.
Finally the chromatic scale given in Ex. 222 was evolved. There
was no D flat, D sharp, G flat, A flat or A sharp, nor should these sounds
be used in writing modal counterpoint.
THE MODES
187
Ex. 222
trpr-
Tf
| o |o o ^
_4*JL
146 Perfect cadences were nominally allowed only on the finals,
mediants and dominants of each mode,* but composers allowed them
selves considerable latitude in this matter. As there was no D sharp,
the triad on B could only be used with a minor 3rd. The Phrygian
cadence was therefore constructed from the triad of D minor, or its
first inversion, followed by the major triad of E, as in Ex. 223. The
canto fermo, or plainsong melody, invariably ended with a -descent of
one step to the final of the mode. It was usually in the tenor, as at
Ex, 223 (a), but might be in any other part as at (b) and (c). Very
often this cadence, if at the end of a movement, was succeeded by a
plagal cadence to give finality, as in Ex. 224.
Ex.223 GO
(J) C.F.
1C
*s=
C.F.
K Q
H
TT
L
.. Is...
c*t
a-
Q
TT
ilii
1 1
C.F.
Ex.224
r-4
J 1
-sM
*r
u
is: .
1 r
Tf
\ '
fi i J
ri
e '
Lj^j :.
b=
'==?
IMI 1
147. At first, when nearly all church music had a modal canto fermo,
the modal feeling was retained in the music. But later on when
music began' to free itself from the limitations imposed on it by the
ecclesiastics, the absence of a modal C.F. and the use of numerous
accidentals gradually drew from it nearly all its modal flavour, and
finally major and minor scales supplanted the modes.
148. The student will find it most helpful to practise the use of the
modes in two ways, (1) harmonizing modal tunes, (2) writing modal
counterpoint in the style of Palestrina and the Tudor composers.
(1) Harmonizing Modal Tunes.
149. Nearly all traditional melodies which date back to the XVIth
century or earlier are modal, or were so originally. Many have been
altered and spoilt to bring them into a major or minor key, just as
many beautiful old buildings have been restored and brought up to
date by people who could see no attraction in the artistry of any period
* The dominant of the Phrygian mode is C, not B.
188
COUNTERPOINT AND HARMONY
except their own. In order to preserve the peculiar fragrance of these
tunes they should be harmonized strictly in the mode without the, use
of any accidentals except perhaps an occasional sharpened third in
the final triad. After harmonizing them for voices they should be set
as songs with a pianoforte accompaniment, using the vocal harmony
as a basis. This must be done when first writing pianoforte passages
arpeggios, etc., to avoid bad chordal progressions.
There should be as few notes as possible.
The accompaniments may be chordal, contrapuntal or mixed.
Rhythmic figures should be appropriate to the style of the tune.
Use ingenuity in thinking out these figures. Keep to the same one
throughout a tune, or to an important division in it.
Do not use repeated chords, they are too common and easy. Write
for one, two or three parts that is where the pianist has one, two or
three notes to play at the same time. Arpeggio figures are only possible
at this point in slow tunes or where there are few changes of chord.
In writing different accompaniments use the notes of the chord
in every possible order 123, 132, 213, 231, 312, 321, but keep to the
same order throughout one tune for the most part. See Ex. 225.
Exs. 226-230 show modal tunes treated in the way described.
Ex. 225
? >
This example only gives the different arrangements of three notes.When the
chord has four notes and the length of the notes is varied, endless dombin-
ations are available.
Example 226 shows how to make a two-part piano accompaniment
complete and full-sounding by embracing two vocal parts in one instru
mental part. Here the quaver passages include the notes of both alto
and tenor vocal parts, or tenor and bass, by dodging from one to the
other. In bars 1, 4, 5, 6, 7, 8 and 9 (piano part) will be found
the 2nd inversions of triads. They may now be used in this way by
the student, that is, when the chord progression passes through them
from one position of a triad to another. The progression must
neither start nor finish on them. This will come later. The ear carries
on the sound of a note over a short rest. Thus, in every bar the ear
carries on the sound of the bass of the piano part over the following
rest or rests, even when the pedal is not used.
MODAL TUNES
189
. Traditional Carol, 'Joseph and Mary' (copyright). Dorian mode, plagal
form, transposed.
The F sharp is ornamental and does not affect the mode (150, iii).
Andante
Voices
Solo
Voice
Piano
190
COUNTERPOINT AND HARMONY
Example 227. Here the piano accompaniment is built on the four
notes of the tune marked with brackets which recur so often, and
always at a different part of the bar and in different rhythm. This
recurrence must have been unconscious on the part of the unknown
composer, yet it gives unity to the tune. Compare the dropping 6ths
and 7ths in Schubert's " An die Musik " mentioned by Stanford in his
book on composition.* The octaves in the bass of the piano part help
to show the form of the tune 4 bars + 44-2+2. In bar 7, voice
and piano version, the quaver G in the tune is treated as an accented
passing note, the chord of F prevailing for the first half of the bar. The
student may now use accented passing notes freely so long as they bring
about either a better movement in the part in which they appear, or a
better chord progression as here, or both. In XVIth century counter
point they may be used sparingly on unaccented beats.
Ex. 7. West Country Folk-song, 'Matthew, Mark, Luke and John' (copyright).
Phrygian mode, plagal form, transposed.
* Musical Compositions p. 39. C. V. Stanford (Maemillan).
MODAL TUNES
191
FE
c;f r
ii i nrn i
Example 228. This tune may be regarded as in the Lydian mode,
or in F major with a modulation to C between bars 7 and 14, (counting
from the first complete bar of the tune). Here it is treated as being in
the Lydian mode, for the B naturals give it freshness and save it from
banality. It is so quick and light that one chord in a bar is generally
sufficient. Notice that between bars 7 and 12 the bass does not sound
till the 3rd crotchet of the bar, yet the ear is satisfied, for the pace
being so fast, it is not kept waiting too long. Notice also the way in
which the suspension in bars 9 and 10 is expressed in terms of the
rhythmic figure in the piano part.
Ex. 228. Czech Carol (copyright). Lydian mode, plagal form.
, Vivace
192
J
COUNTERPOINT AND HARMONY
ins-
Example 229. This is partly chordal and partly contrapuntal.
As in the Dorian example the right hand part of the accompaniment is
lormed from the alto and tenor of the choral version. It is given some
degree of unity by the recurrence of the figure in bars 2, 4 and 5.
Ex. 229. English Carol, 'Righteous Joseph' (copyright). Mixo-lydian mode
Poco allegro authentic form '
MODAL TUNES
193
Example 230. The accompaniment figure consists of the three
notes of a triad plus a passing note. The two quavers on the third beat
followed by the crotchet on the first are to be found in the tune itself.
Notice that the right hand is sometimes given five quavers instead of
three by design and not by accident, for these occur at the end of the
phrases in each case.
It will be noticed that the piano parts are complete in themselves j
that is, they are for the most part in good two-part harmony irrespective
of the melody. This is necessary when sounds of totally different
timbre are concerned in the ensemble ; as, for instance, when writing
for the brass in the orchestra. Their parts must sound well alone,
otherwise they are not likely to combine well. A melody is regarded
as complete in itself. Thus, the modal tunes in these examples are
beautiful and sound complete without accompaniment. Similarly
if the brass play a melody in unison the effect is satisfactory.
O
194 COUNTERPOINT AND HARMONY
Ex. 330. English Folk-song, 'I will give my love an apple' (copyright).
jBolian mode, plagal form.
Andante
c_r
MODAL TUNES
195
196 COUNTERPOINT AND HARMONY
Exercises on the Harmonization of Modal Tunes.
First harmonize the tunes given below for four voices, and then
write piano accompaniments to them. Suggestions are given for the
' style of the latter, but they should also be written with accompaniments
entirely invented by the student.
English Traditional Carol (copyright). Authentic Dorian.
Allegretto
m
MODAL TUNES 197
2. Old German Tone, 'Auf den neuen Jarstag* w.Figuius(i5<#). Plagal Dorian,
transposed.
Allegretto
f , P
s
r Tr
j IT I I I J J J rtj > r
3. Ancient Irish Tune, 'The Battle of the Roe* Authentic Phrygian.
Andaate
rrr
198 COUNTERPOINT AND HARMONY
4. Ancient Scottish Tone, 4 0n Ettrick Banks! Authentic Phrygian.
Alia marcia
ifc
tin
(1) The triads without 3rds are in keeping with the austere
character of the tune.
(2) Plagal cadence.
MODAL TUNES
199
5. Lullaby of the Nuns of Chester, (copyright). Authentic Lydian.
Andante
t r r F ir r
6. Irisli Folk-song, (copyright). Treat it as being in the Lydian mode.
Three slow beats
(I) A suspension prepared in the accompaniment bu\ not in the voice-part . The
zrries on the sound of the quaver A, as shown by the small note. See notes to
ear carries
Exs. 226 and 228.
200
COUNTERPOINT AND HARMONY
7. English Folk-song, 'Seventeen come Sunday '(copyright). Plagal Mixo-lydian.
Vivace
iU t J t
m
i
J 1-iJjUJJj
8. English Folk- song,* The Bonny Bunch of Roses, OP (copyright). Plagal Mixo-
lydian.
Allegro (2)
RF
:=F=F
~
-
zz
^
=ff=
J n|irntf^=c=
f
"T
f 3
F^H
J=
-*-
^
i
j
., 1
L, ,.f
N=
p
1 v^
S^
i ' *
(i)
-=#=
TTf
J4-
^
-i
^^
rff P
^p=
fA-
*-
f^-
I
^^
iF=f=i
^S
P~d h
y=i
=
-
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J P j J*] "I 1 r-r-H
U
t=s-
=5=t
i
-1
r j j M
(3)
^f- ~ J Mi
1 5- 6- *
-
- (1) AV?
fore because a
fl continual flow of quavers. (2)
semitone is obvious and natural.
jF sharp is not in the mode, but it occurs
(3) The titne finishes on the dominant.
MODAL TUNES
201
9. English Folk-song ,'A lawyer he went out one day' (copyright). Plagal AEolian.
Andante grazioso
p
' r
r
10. Irish Folk-song, 'The Star o' the County Down'. Plagal AEolian, transposed.
Andante
i
jiujj jiJiiJ j
(1) Maintain the undulating quavers by means of passing-notes and untied
suspensions.
20*2
COUNTERPOINT AND HARMONY
Further modal tunes to be treated in the same way. The student
must find the mode and invent the accompaniment.
Old German Tune.
(Copyright
ijjj iJJr i r fJ iJJ
English Traditional Carol.
(Copyright)
Netherlands Carol.
(Copyright)
rrnr r if fr u JuJJi r r u
English Folk-song, 'Glencoe\
(Copyright)
7rwA Folk-song, ( The Brown-haired La$s ! .
$mjMnJt W'j"3j|iJ J'JTjjiJnjij j,!^ j J
Other modal tunes given in previous sections should now be re-
MODAL COUNTERPOINT 203
(2) Modal Counterpoint.
150. The two main points to be observed are as follows :
(a) Accidentals should only be used as they would have been used
in the XVIth century.
(b) The mind should be freed from all thoughts of major and minor
keys.
(a) Accidentals.
As has been shown, accidentals were used (i) to make cadences,
(ii) to escape from augmented and diminished intervals melodic or
harmonic, (iii) in some cases to flatten the middle note of three where
a part ascended one step and returned, or to sharpen the middle note
of a similar descending progression.
(i) Cadences. These were, as now, perfect, imperfect, plagal and
interrupted. The perfect cadence had a major triad as its first har
mony, followed by either a major or a minor triad as the second. At
the end of a movement, or important division of a movement, the final
triad was always major. The plagal, interrupted and imperfect
cadences differed in no way from those of to-day, except, of course,
that they were constructed entirely with triads and their first in
versions, passing notes and suspensions.
(ii) Augmented and diminished intervals. Those who have
taught singing to people without previous experience of music, such
as choir boys and some chorus singers, will agree that by nature they
have great difficulty in obtaining a perfect intonation of the chromatic
scale and augmented and diminished intervals, and instinctively rebel
against them. Mr. Cecil Sharp noticed this when he persuaded country
people to sing to him their folk songs. He wa^sometimes at a loss to
know whether they intended a flattened or a sharpened leading note,
so uncertain was their intonation of the semitone. Although augmented
and diminished intervals are not found in Palestrina, they began to
appear in Tudor music towards the close of the XVIth century.
(iii) The upward or downward step of a second. Here again
natural, untaught singers have a distinct tendency to make a semitone
instead of a full tone when there is an immediate return to the previous
note, and this was no doubt the reason why such progressions were so
often semitonal in the polyphonic period. It must have been instinctive
in the singers to put in their own accidentals, and that is why com
posers left it to them to do so. It is often difficult for us to determine
exactly what they intended. Sometimes they wrote the two sounds
of a chromatic semitone to be sung simultaneously, making discords
that sound harsh even to our ears.
204
COUNTERPOINT AND HARMONY
(fc) Avoidance of Major and Minor Keys.
To write music which has the true modal flavour it is essential
to rid the mind of any thought of keys or modulations. The use of
accidentals solely for the three purposes given above will broaden the
student's scope in the matter o harmony, for it will bring into juxta
position triads which would never be contiguous in diatonic keys.
Freedom will also be gained from the tyranny of the dominant dis
cords, and the constant use of the dominant, tonic and subdominant
as the roots of chords. Very much modern music, when stripped of
its discords and analysed, will be found to rely on these notes for the
basis of its harmony just as much as did that of the Victorian age.
The modes, moreover, will teach us how to use chromatic harmony
without becoming sentimental and effeminate.
151. The following short examples, one in each mode, are given to
make clear what has 'already been said. The numbers refer to the
three uses of the accidental. In most cases two forms of the music
appear; one in the mode and the other in the corresponding major
or minor key. This is done for comparison.
152. The Dorian Mode. Ex. A (1). Music in this mode differs
from that written in D minor, for B natural will be used whenever it
will not entail a departure from the rules as to cadences, awkward
intervals, etc., given above ; and B flat will never be used except to
avoid an awkward interval, to make a plagal cadence on the final or
mediant of the mode, or, in some cases, when a part has the progression
A, B, A. The accidentals in the D minor phrase are obviously used
because they form part of that scale in its two forms, harmonic and
melodic. If the first and second bars had stood as at (1) with the
addition of B flat, there would have been a modulation to F major.
Similarly, at bars 3 and 4, if B natural, G sharp and C sharp had been
used, these notes would change the key to A major ; also the F sharp
m bar 4 would have put the music into G minor. No such modulations
occur in (1). The progression at bars 3 and 4 is not a modulation to
A, but a cadence on the dominant of the mode. Bars 2 and 3 contain
an example of what would now be termed the chromatic chord on the
flattened supertonic, the first inversion of which is now known as the
" Neapolitan 6th." (See Section XIX.)
Ex. A. (i) Dorian
MODAL COUNTERPOINT
205
153. The Phrygian Mode. Ex. B (1). As a perfect cadence was
impossible and as there was no means of sharpening what we should
call the leading note, the Phrygian mode had a more modal flavour
than any other and kept it despite the unrestricted use of accidentals.
Ex. B has a cadence at bar 3 on the dominant of the mode (C).
Ex.B. Phrygian
154. The Lydian Mode. Ex. C (1). The sharpened fourth degree
gives this mode quite a distinctive character and makes it less like F
major than the Mixo-Lydian is like G major. It is quite probable
that the use of the B natural just before the cadence, especially when
the | chord on the 6th degree was used, gave birth to the modern
chromatic supertonic 7th, see bar 12 in the example, and compare the
harmony of the first phrase of Schubert's " Ave Maria." This mode
rarely appears in ecclesiastical music.
Ex.C. (t) Lydian
206
COUNTERPOINT AND HARMONY
155. The Mixo-Lydian Mode. Ex. D. This mode became
very like G major, because F sharp was constantly used for all three
purposes mentioned above. Ex. D should also be played with the
signature of one sharp. The student will now realise why modulations
can be made without accidentals (81) ; it is a legacy handed down to
us from modal times. Ex. D seems to end quite satisfactorily in the
key of G, as did Ex. 66, although there is no F sharp.
Ex.D. Mixo-lydian
156. The JEolian Mode. Ex. E (1). .This resembles A minor
more strongly than the Dorian or Phrygian modes resemble their
modern minor prototypes, for G sharp has to be continually used for
the perfect cadence. It was rarely used in the XVIth century.
Ex.E. a) AEolian
MODAL COUNTERPOINT
207
157. The Ionian Mode. Ex. F. This has actually the same
notes as C major. Even so XVIth century music written in it does
not sound like music in that key. Ex. F is an endeavour to make this
clear. It is very unlikely that anyone who had a knowledge of keys
only would spontaneously write thus, yet the F sharps and the G sharp
are natural enough modally. Incidentally, the double counterpoint :
i.e., invertible counterpoint between tenor and alto, treble and bass,
would have been impossible in C major without modulation. Much
of the difficulty caused by the awkward intervals in a minor scale (56)
vanishes when accidentals can be freely used to avoid them. The
amazing thing is that these accidentals do not give to the music the
restless and purposeless feeling engendered by too much modulation.
Ex.R Ionian
i 3
r f<
J
A A
158. It was stated in (140) that one advantage of a knowledge of
the modes and of Musica Ficta is that it shows the origin pf many
things in counterpoint and harmony that would otherwise be inexplicable.
Even at this early stage five important points have been elucidated
(1) why a 4th answers a 5th in a fugue subject, (2) why changes of key
can be brought about by cadences alone, (3) how it came about that
the chromatic chord on the supertonic can be used without causing
modulation, (4) how accidentals can be used without giving the effect
of incoherent change from key to key, and (5) how the chromatic major
triad on the flattened supertonic originated.
208
COUNTERPOINT AND HARMONY
159. Transposition. Only one kind of transposition was allowed,
namely, a perfect 5th lower, or a perfect 4th higher. The signature
of one flat, B, was used, and the Dorian mode then began on G, the
Phrygian on A, etc. Modern editions are often misleading. The pitch-
was a minor 3rd higher in the XVIth century than it is at present, but
this does not seem to have been generally known until recently. The
latest editions are properly transposed a minor 3rd higher, but some
of the older ones are in the original keys, or are only raised a whole
tone. Some of the examples given in the previous sections of this book
have been transposed a minor 3rd higher in order that the voices should
keep to their proper compass.
160. It is necessary at this point to explain two exceptional uses
of discords. The first, the Nota Cambiata, or changing note, is found
frequently in both Italian and English music of the XVIth century
The other, sometimes called the " English Cadence," is peculiar to
this country. The Tudor composers used it so frequently that it almost
became a cliche with them. Moreover it persisted long after that
period, as is shown by the examples.
*EE
Ex. 230( a ) Ex.23, a} , ,,,
g II I fl .. a) I. ***"".. . fl . ff _ . _
ibid.
Ex. 232
Ibid.
Ex.233
1 Ibid.
Ex. 234
Ex.235
HTF
7
4
^
^
-0*
-e-
**
J
U
ft)
ff
V no ll.l J E
MODAL COUNTERPOINT
209
Ex.236
m
Tallis
Ex.337
-
T
d
161. The Nota Cambiata consisted of a four-note figure, Ex. 230 (a).
The first and third notes were consonant, the second was dissonant,
the fourth was sometimes a harmony note, but often a passing note.
The second note is the exceptional one, for it is the first appearance of
a leap from a discord and the first case of a delayed resolution, as the
dissonance of the second note is not resolved until the fourth.*
The Nota Cambiata may be regarded as the progenitor of the many
types of ornament formed from the notes immediately above and below
a harmony note. It was most commonly used at a cadence, either by
itself, as in Ex. 231, or, more often, with a suspension. In Ex! 232
the suspension is resolved before the occurrence of the Nota Cambiata,
whilst in Ex. 233 the two occur simultaneously. In Exs. 231 (b) and
(c) Soprano and Bass and 233, the 4th note of the figure is a passing
note. Nota Cambiata must not be confounded with the same figure
shown in Ex. 234, where all the notes are regular ; the first is the
percussion of a suspension, the second its resolution and the other two
ordinary harmony notes.
162. The essential feature of the English cadence is the combination
of a suspension of the tonic over the sharpened leading note (or, in
XVIth century language, the suspension of the final of a mode over
the sharpened 7th degree) with another part moving by passing notes in
a downward direction commencing on the 7th degree, which is usually
flattened. Ex. 235 (a) and (b) of the English cadence fulfils the rule
given in (135) for, if the suspension is eliminated, the other three parts
are in consonance ; but it doubles the suspended note (124), Ex. 235 (c)
and (d) shows a new departure, for here the flattened 7th degree becomes
an accented passing note. Accented passing notes are occasionally
found in Palestrina, but only on the weak beats of the bar. This
treatment of the flattened 7th degree still persists.
The English cadence is typical of the XVIth century English
composers who were continually experimenting with new forms of
dissonance. Exs. 236-239 show further forms of it. Exs. 240 and
241 show the use of it at the end of the XVIIth and the beginning
of the XVIIIth centuries, and Ex. 242 in the middle of the XlXth
century. Ex. 238 Byrd
s.
[%-,-f | ; . r 1
A.I.
A 2
$fc^
ft
r
^ f
iyj
T.
[ <> is [^
Ji
(-
-j
i j ri i
B.
=41=^
n
K f i r
* The first note of the figure is always three times as long as the second. The other
two vary.
210 COUNTERPOINT AND HARMONY
EX.339 Byrd EX. MO Parc.ll (858^695)
3
k
" ^ J J
- '
**
m
-
:3Z2
Ex, 341
Weldon (1676-1736)
Exercises in the Modes.
Insert appropriate accidentals in the first four exercises.
1
jj^ ^
J "H
f
>>
T 1!
1
rt
^
1
r
J
? o
|J-^-f
r
-^j
*
,
C
y- p
t a_[i
!
MODAL COUNTERPOINT
211
iil
Tff
J J
-5: Q
^ ^ j T
r a / jj
-O
O
O "" M..^*^ ^ | v*
\>\ J H
"-f 1
19=
JM
M
f
M
^^
- o
"rr
y ll
4*
I/O Je "
ru -sa - lem, Je
Palestriua- Lamentations
ru - sa - lem
1
p u - ^
dgb
r^
61
"~T
Je -
1 Jj., |
ru
IJIU-
a IM
1 o 1
^}
Z1
?-5
r%4r
159
212
COUNTERPOINT AND HARMONY
Je - rn - sa - lem,
I Jf. 1 1 1
4=
-sa - lem
r-K -H
r f trr '
Je-ru ^ -'
E|^ i S' o
J
^
lem,
sa
"f
ID
^'rr '
^u
....
BF31
^v
B e 1 '
HN 1
91 _i
/. con - ver - te - re
ad Do - mi - num,
ad Do-mi - num De - um tu
um,
ik.r'TnfiNirr 1 7Ja
ad Do -mi - num De
am tu
um.
Example 243. This contains no counterpoint, but the harmony is
typically modal. The B in bar 2 is printed as a natural by Boyce in
his collection of cathedral music. Probably it was sung as a flat
(150 (iii) ). It certainly sounds fresher as a natural. Boyce took out
the 5ths in bar 3, altering the passage as at Ex. 243 (a). Notice the
arrangement of the cadences :
Phrase 1. Perfect on Final of the mode.
2. Perfect on Dominant of the mode.
3. Perfect on Seventh of the mode.
MODAL COUNTERPOINT
213
Phrase 4. Perfect on Fourth of the mode.
5. Half cadence on Second of the mode,
6. Perfect on Final of the mode.
7. Perfect on Dominant of the mode.
8. Perfect on Final of the mode.
9. Plagal an Final of the mode.
The " false relations " (85) between the end of one phrase and the
beginning of the next have no bad effect (bars, 2, 4, 10, 11 and 13).
Ex. 243
Anthem by Adrian Batten (d. 1637)
Dorian mode.
I p 1 , p 1 1
i i j =
j Kt
De -
^H
.J ,^,,," . ,_ . U , _
^ : r iff r
liv - er us,
__. 5) _ ^ $J
-s w # .
r if *P
Lord our God,
i~
and
+-
-H-
<^3r if r f ;
ijhjj. J J j j
r r r
1 . L J 1 =4=
v r
r Ii
J j .hi
3 (* r f r r f * r
ga - ther ns from a-mong th
J. J * * J- J
* i ; :j " S ? P P "
he a -then,
J J
that
* * \
f iff
we may grse
i-' f P- P r r r r
p
[2 W"
r r' i j=d
iJ J. J .= .J .i.
J |A,J 1 1 1-4-
m.
* I
th
p .. p . .. . .-
anks un - to Thy ho
J. ^ 4 A
r-
- iy
rJ
Name, and make our
-t-
Tt-
|^T [
f .- L ' _ L
1
13 r -r ^ r 1
4-
jf *|
H J ,
1 J
TO Yfe e r e
J * f f TT
hoast of Thy praise.
.._... J O.._...o- r*
f
B
H-^
Less- ed I
e tl
b.e Lo
? v* F"
rd God of
3=$=
'=3
& 1
p
< r r
^
Is - r,a - el from ev - er
J ^ rJ J
F F
last - ing and world with- out
^=^r
r
3E
r
peo-ple say A -
fr- r r f- p
men, and let all the
end. And let all the
^
S
214
COUNTERPOINT AND HARMONY
Ex. 243
7P?
J J J
T" ' 1 J
*nf
U
r r
is from a - m
^>
-. " p
ong the
J- J
f
r
Exercise 5. Add Alto, Tenor and Bass to the first part, and Soprano, Alto and
Tenor to the second. Write in the Dorian mode in the style of Ex. 48.
r r ir i
De - liv - er us, Lord our God, and ga - ther
us from a-mong the hea-then: that we may give thanks un -
^
*
- to Thy ho - ly Name, and make our boast of Thy
j
praise. Bless . ed be the Lord God of Is - ra - el from ev - er
last - ing, and world with- out end: and let all the
m
peo-ple say, A - men, and let all the peo-ple say, A -
- men,
Exercise 6. Write an Anthem in the Dorian mode modelled on Ex.243.
MODAL COUNTERPOINT
215
Example 244, Examine carefully the imitations by inversion in
this Example. Observe the way the subject and its inversion are
distributed between the parts, so that no part has the same theme
twice in succession. Note the accidentals and their effect, especially
in the last three bars.
The words are those of the ninth verse of the Magnificat. The
form is dependent upon them, for each new verbal phrase has a new
theme. There are, however, no complete stops as in Ex. 24-3, for
Palestrina starts his new theme before the previous one is complete ;
or, less often, the moment it is finished (bars 16-17).
Ex. 44
From Palestrina's Magnificat on the Second Tone
Dorian mode, transposed.
H?ii \ " "* 1
TfrMf 1
Sn
'"' f=
see - pit
mn5
J c
**" B "
Su - see
-W= A
= f r * =g=
pit Is - ra -
1 w cj; _ r ,^\
el pu - er - um
==^
A
J
IPl ^T '* 1
^nfl
F . f f p 1
Is - ra- el.
=
pn
J_-
==
. er-um
~P
sn -
lit) * 11
Sn .
Bl J J f p g-
F
see - pit
=3=r= n j=
" 4
Is-ra
.el
- p-p-j
fH-^=-
pu . er-um
..^f *..|_ I P..J
su
^J* ,
J * 9-4-9
"-
nm, su
-=fcJ
1
f '' i
um,
- U 0-- J
^4
-O-s
-3 H
^=2
Su
see - pit
10
ra- el.
IEU r " ~i i
r o
iifi ji r r
r
um,
-" ^ '
F [ r I
Su
- ^
= r r r 3
um, su
| J =q
nm,
*y . ^
Su
-e-. J 1
see - pit
h= 5P m P
F .. -
Is - ra - el
|-f m *-*- If p f
J^-i
1 f f
H-f IL fcdH :
pu - er-um su
216 COUN
BJI * " IA
TERPOINT AND HAKMUJN
-
i ^ n _ n ... n
Y
r r g p 9
Su - see - pit Is - ra - el pn -
'M f
er-um su -
S
TJifrp fr= p p * i
OL C -\
u - sce"^ 1 ^ pit Is - ra -
u " g <>* J g /'
el
-= g-s =
-[- 1 f- 1 L-L
ptt- er-um Su
*^ " s
=- f J 4= e
um,
1 Q
r ^-
pu - er-um
^r r *->
N urn,
-/ 15
fS^as
Su -
rlKH rM
see - pit
fab JL_^
um,
r
su - um, re - cor.
J J f ,. ft- ^ " f
^' f r=
pu - er-um
118 ij -. J 1 i
__J J_2 2 p
su - um, re - cor-
~ AJ <& = 1J P TT! 5 1
IP f * ^ -?
eu -
) ; i J Jt J J 2
_ r == r^^J
um, re - cor - da
1 J J 1 o II" P If" ,}, 1
,/ i? g flrJ 5 SUq-.,- - gt 51 1 f
""N Is - ra - el pn - er-um su - um, re cor - da
S 20
Wh T^ p- ** a "J *
ffi^ (.
-da -
K^ r iTl* |=F
tus mi - se-ri -
--a ^ *^ "-M ^ y ^Z
1
cor . di-
Vip, p ^
ia p-jLp g__ _ 1
- da - tus mi - se-ri- cor - - di . ae su
||gi, | 1 ^ n ^"^r.. r
"or i
- ae,
J j-l
jia &z d
^ - tus mi
*Jri 5 = 4-
h ^^
- se-ri- cor - - di - ae
1 1 1 p e
o " ~ rJ & "\
SU
^b fi^ ^ e ^ |
"N -tus mi- se- ri- cor~~~- di - ae
J 25
11 .)
su - ae,
- ae su
BO rf =
ae, mi -
r p p m p
se-ri - cor -
|g| r r - =
mi - se-ri - cor - di -
* -a p "-* 19
ae su
a P* hp* p
IK i -i j^-pp=p
1I " R f.... rf Jj J.z-
Hrr
rrrs 1 P-
ae, mi- se- ri - cor - di -
j j= -
E r H [f
ae su
-^ ^
^_t
>
O = O-s 1
mi - se-ri - cor - di-
ae su
MODAL COUNTERPOINT
217
30
m
*fl=
di - ae
sn
=wt=
- ae, sn
BE
ae.
N ae,
sn
ae.
Exercise 7. Fill in the missing parts, taking Ex.344 as a model, Dorian mode.
J* . =q
I
w
^
Sn
lit ^
see - pit
F^
-III
i 1
So - see
*4Mt ,
=a J ^ ..-j -
' - pit Is >
V |J ^ ^=^
ra - el pu -
-i-3
rr
-fcff
l=|
= L g " *
W-73
^ I
*-
5
7 a
1
ra
el ^ p ""
.. ~ ?p'
pn -
s
n - see
I i i i j i
|J J |
J J J > .
er - nm
S
n
X i ft
nm
o 4
*-
Sn - see
pit
r^^ r
er - nm sn
nm
Sn - see -
Is
ra - el
pn
er -
218
COUNTERPOINT AND HARMONY
i
^ . um sn
nm, sn
am, sn . see -
pn
pn
i
" r.
pit Is
ra - el pn er.- nm sn
[1 -Jj
=M
o-
_
T J
-
i e
^
i c . J -=|
& ; 4
* re~
Id p 1
^ 1
oor- da
-f
-
[_e i-^. ..,]
tus__
re - cor -
3=
1 :
: ,
*-* a fl i
, ,
3=
! ,
mi - sa - ri
r-H" H
1 " '",
1
"f
[ - -f" .
-um re - cor - da
tns
fjL j j
^=^
-j
1 i I
I j ;== i
ty~7 sL
^rl mi
us
-S
sl J-
;e - ri
-
ce
>r- di-a
-
sn
ae, mi-se-ri-
IS
cor
-MS
li
a
e
|[ -J*
MODAL COUNTERPOINT
219
i
**:
=
-cor - di- ae
sn
ae.
Exercise 8. Write a movement similar to Ex. 244 and Exercise 7.
The words may be Latin or English, but the former is better suited to
this style of counterpoint.
Example 245. At bar 10 is a theme in which Nota Cambiata is
used. It is rarely found in the lowest part, out an instance will be
seen in Ex. 246, bar 34. The cadence is described in (146).
Ex. 45
From Palestrina's Fourth, Magnificat* Verse 3.
Phrygian mode.
__ __
t
Bl
y
Qui -
a re spe - xit
e *J B <* B
Qni -
a
i F
re . spe - xit hn - mi - li -
jEo-a
Qni -
ll A 11 ^ '
a
re
-
spe - xit hu- mi - li -
j
Qni - a
c 5 , , .
re -
spe -
xit iin - mi- li - ta
k
\
fe r r *i
^ feu-mi- li -
ta
- 1
lom an ~
i
^ F
-ta - tern .
4af
^
an -cil-lae sn
; | .,* ^ ,^j- ff j ^
g
i
p
. ta - tern
in-c
il-li
i
ie su - - ae,
L^-p-L? ^S. i:^ e
^
-tern s
ia -
<
5il-l
ae
sn
~T~ ... n . '
220
COUNTERPOINT AND HARMONY
10
rar jr- 1 j i 1 j r
d i
^ - cil - lae sn
lfi> j j . j j=^
-.-J ^ jH
_ *
-IMI
ae:
If) i i
H*T ^ 5 lh"i P f
-e
ae: ec -
ce e -
ran .
"' f J , r r
an - cil -
lae su
lioil
ae:
= = 5; &
"\ - cil - lae sn
ae:
f r r =
Ec - ce e .
ec - ce e
nim ex hoc.
^
^
ce e mm ex
m
nim ex
s* 15
hoc
ff=f
[
i ..
1
^~^
JL
4*
1 6
be -
>~
a
-9
tarn me*
^ e 1
di . cent
= fi> -J
>
f^
J5
i
S r ^
S
be -
CT
a
s*~*
tarn me
di
rj 1
^ =
cent om -
hoc be
==1 i
a
^
tarn i
-N.
ne
di
i
[r - -'
be - a
tarn me
di - cent
20
1
om-nes ge
ne . ra - ti
9 * -*
o
-frf
f
- n
es ge - n(
LJ _
3 -
r r i
ra - ti -
3
*
1 1 f '" '
IL
E*^- .
-
i
-
C
>ent
d
om - nes ge -
-
MODAL COUNTERPOINT
221
=3
*=
r | 1
f
-ff
h
a
-
-
nes, ge - ne - ra
lr' __p P f^
ti - o J - O
f
1
-
J y
-
[~ L p 2 *-* -
-p , j
nes,
f * 9 p
-
J r
ne - ra -
ti -
'I cr J \ rj
-H- r
V
om - nes ge
=' r r r =
ne - ra - ti -
25
i r
& J J U J
115 " J ' J j |
Uefr -I
nes. ,
rl i l 1 r
m=: '
_P.
om - nes ge
1 J ftj J ^=4
^ * ,.
ne - ra ti -
uk 2 J A
tieH
_|9_! Q
i 4MI- -41
nes.
IP r i
- nes, om -
F
nes ge - ne -
T [
ra - ti- o
nes.
^JL
1 J CT ;
nes ge - ne - ra - ti - o
nes.
Exercise 9. Fill in the missing parts, taking Ex. 345 as a model
I
r i" r
For He hath re - gard - ed
the low -
Bi
? F
1 1
P* f 1
f
!| 1-
>
| 1 1 1
1 =
If
X
-Ms I
-4
=*==
. L j-^7 y ^-^
It ~^" \
Li-nf
5SS.
K 1 r - | -|
fhe low-li-nesR of Ills..
222
COUNTERPOINT AND HARMONY
Trrr r
of his hand - maid
en
i
for be -
m
r r ir r
^ hand -maid- en.
of his hand -maid- en, for
1?
f
"X
= f
or be -
hold
-hold.
t=l
s* ^
x
-U 6 .
for
4 F -
> be hold from hence - forth,
J t
for
rf
- 1
_,
F^=
_
1
itf
, *L *
all g
e -
ne -
1 *
ra
'
1
tions shall call me
w
f
i
1
I
1
-p
a
\
1
1
P^ i i i
I I J j I i :
bless-ed
j J J
all ge -ne -
J * * J J
ra^~"^"~^ tions
- f f f =
rTfr'
r J
1 1 1
all ge-ne -
1
ra - tions
kp==
MODAL COUNTERPOINT
223
all ge - ne - ra - tions shall
call me bless
ed.
I
Exercise 10. Write a movement in the Phrygian mode on the
lines of Ex. 245 and Exercise 9.
Example 246 is a typical Palestrina motet. The form depends on the
words. Each verbal phrase or half-phrase has its own theme. These
themes are treated (1) harmonically (bars 37 and 68) ; (2) as points of
imitation (bars 21, 26, 39) ; (3) canonically with imitations in the parts
not concerned in the canon (bars 1-17, 52-67). The Coda in \ time
(bars 68 to the end) might be taken as the progenitor of the modern
simple, quick and jolly last movement. Nearly every section dove
tails into the preceding section, for although there is a cadence at the
end of each, the new one begins before the cadence is completed. This
is a most important feature as it gives life and continuity to the music,
and prevents it sounding like a number of separate slices sandwiched
together an easy thing to happen with so many different themes.
There are only two full stops, at bars 36 and 67. Even these do not
give the impression that the composition is complete, as both end
with cadences of an imperfect character.
Special or unusual features are as follows :
Bar 15. The tenor leaps to a note (A) which is not in the chord.
It is a note, however, which is consonant with the other moving part
the bass.
Bar 30. The bass enters on a strong discord, the three other parts
being suspended. Tfre suspension of the whole chord is uncommon.
224
COUNTERPOINT AND HARMONY
Bar 37. Note the fresh effect of the triads of A minor, G and F
in succession, and how any crudity is avoided by the contrary motion
by step in the outside parts, (20) and (34).
The following is a rough literal translation of the words :
Dies sanctificatus illuxit nobis :
The holy day illumines us :
Venite gentes et adorate Dominum :
Come ye people and adore the Lord :
Quia hodie descendit lux magna in terris.
Who to-day descended a great light to the earth.
Haec dies quam fecit Dominus :
This is the day which the Lord hath made :
Exsultemus et laetemur in ea.
We will rejoice and be glad in it.
Ex. 246 Motet, 'Dies sanctificatus'. Mixo-lydian mode.
Bi - es sane - ti-fi-ca - tus
il - lux-it no -
bis, di-
-lux-it no
.
bis, no
bis, di
il i i i i
i
p
Q8 sanc-ti-fi -
j' v
! g --ji v P .
ca
u r r P i
tus
j9 n
a ' 1
ff
' r i r 1 r=
}-. a. -
es sanc-ti -fi -
ca
*-
t
us
-irq
r r i
il - lux - :
it
5
- ca - tus
g r
i r f i
il - lux-
it
no
b
H
is,
c j r r *
il - lux
^S a on A -H ^4
-
tus
il-lux-it no
MODAL COUNTERPOINT
225
A 15
lux- it no - bis: ve-
or - a
- te Do
-tes, et ad - or - a - le
mi -
tes, et ad
or
- a - ,te Do
tes,
et
ad
COUNTERPOINT AND HARMONY
\l 1
^P e
ft "
^ Do - mi -
'num; qui - a ho -
di -
mi -
num: qui - a ho
-_ =^^=^ a =:^= f :
di - e de -
- - mi -
-M; o o
1 u_
num: qui - a ho
m IfeB u j 1_
U L-1Z
di - e
rr^ ? \
^ - - mi -
r'fl 40 r
num.: qui - a ho
> r
di-
*- - e de -
seen - dit lux
i>- P p rT> p p f .
ma - gna in
ffi (^ P -j 1 1 1 i
- seen - dit TUT,, ma-gna in
ter -
f r r f i
de-seen -
-H 1 1 1 1 1 ! \.
dit lux ma
f_l 1 !
^na in ter -
* i
^L
- e
de - seen - dit,
MODAL COUNTERPOINT
50
227
a. Ill III i
-flju-*
r. 4 d i n
de-seen - dit lux ma - gna in ter -
m F
-gna in ter
-JMJ *J. -,. _,., ,
Til
rTf- r o-^^> ff .^^,
^ =^ f- - ** 1
in ter - -
-*E o ** 1
ris, Iny ma, . gun, in , , _., ter -
=: o # B ^^ -^
|| * .- 1 f-| 1 =i ..,.| IML, 1
^ lux ma - gna in ter ...
y / 55 - ^
Jl li -il 2 k * * ^ -3
Hflh ==
" -T"IR, ftaftc ... ,
1 -^
rfi PQ iinflTn fp-^.it T)n
IMI r> ^ f3 fl ' *P ^ -
IP 2 h * F 1 1 F-*-
Haec
1 1 1 ! 1
di - es, quam f e - cit Do
T f^- r 1 1
1" i rr r -_
118.
^nr* e
1
Haec di - es,
-e-
4j B 1
jT
\ -ris. Haec
r / ^ / ^ j ""
-jjL p_ u
di - es,
__p &i J., J ^ _> 1^^
I m 1 1 I r 1
IIP P ^ F p
--4- n- - ^-^^..^33 ,JEJ_ - :
mi - nusT*" rrrr:
iC r f f if r r'f I- r- r ^
- mi - nusquam
-- 1 I -f -F- f i
fe-cit Bo -mi - nus,haeo di ftR .
-HWF p^ -TT p^ 1
-*^ ,
ffa.fir. , , di - es^_^
1 2
A
y 60
J
haec
tr n e SL-^ a M 1
*- . .
E_4
Haec di - - es quam
P r o i i r i : ^_ i
Huamfe-cit '.
j \. i i
)o-mi-nus, haec di - - s
f-JJ * - |f 9 = *
qnam fe-cit__
^y^^ n r*
ii_ ttpzt^l ,-
_ Do - mi-nus, t[uam
LJQ o~~ pQ -,.^^ k _ |
J*
A A\
A a iiia,Tn fd -
228 COUNTERPOINT AND HARMONY
j fl o 65
*> fe-cit Do
K - r r r i ~ r i f
mi
? - r r *f
1 II 5~"
nus.
-flf 1 ' ! !
quam fe-cit Do -
1 P H-Mf=
mi - nus.
IMI t-jfc
f ft - ft it. T)
o - mi
l-E
nus.
1 Ml ITJF
*> " ir* rF r r
^ - cit Do
l-'fl 70
mi
nus.
*J Ex - sul - te - mus, et lae -
E% r i r T f i
te - mur ]
in e -
& ftp 1
Ex - sul - te - mus, et lae - te -mur in e -
BK ff F 4- e 6> f- * ^
JttLg ! (I ! 1 [I
Ex - sul - te - mus, et lae - te-mur in e - a,
S Ex - sul - te - mus,
I'fl 75 1
** -^ ,^L A t laft
- te - mur
me-
if i
4S i f .~ J * p u j i
-a, ex -sul - te - mus, et lae - te-mur in
J
e
-e p
ex - sul - te - mus, et lae
- te-mur
-j-nt p 1
in e -
a __
\ ex sul - te - mus, et lae - te - mur
^6 i 80
in e -
U &^ e J 5 p
v -a, ex - sul - te - mus, et lae
te o * -o- J- 1 * p ^ P-
if" J
- te-mur
-==' p^
in e -
*>x
Ifi 1 U
- a, ex - sul - te - mus, et lae
I F
- te-mur in
_ e
- a, ex - sul - te - mut>, et lae
- te - mur
in e -
V - a, ex - sul - te - mus, et lae
--==
- te-mur in
e - a,
MODAL COUNTERPOINT
229
85
U i |
1 ] \ n
-Ls^ Jjv^ L-T.O y
IK? 1 1 T^ F"
--T p p rtn 1-
-a, ex-sul - te -mus, et lae -
|m * p p o p
. te - mur in e a.
.- ri S. a e j^- LI
-a, ex-sul - te - mus, et las'
1 i -W
te - mur in e - a.
^ ex-sul - te - mus, et lae - te - mur in e a.
Exercise 11 Fill in the missing parts, taking Ex. 246 as a model
Aj_g e d p tLz J^ J -f... J
^ Di - es sanc-ti -fi - ca - tus il -lux-it
Di - es sane - t
i p ^ 1
i" - f i - ca - tos il -
*\
.^jL jg ^ ^ J ^ ^ jj * f ?
1.. J I I 1 1
v no - - - _
IK> *p |- f 'Tirrn*^^
|* F dy;|tt O J
-lux- it no -
..,_(J I L [J H| 1
Ms,
-*^
Di - es
A,
t
Di -
*
il -
1
P r r ' * r f )> f T
^ " p r f ^t*J ^ -
sanc-ti - fi - CA - tus
.j ^ fin 1
il-lux-it no ' - ' -
V - es sane - ti - f i - ca
tus il - lux-it no -
COUNTERPOINT AND HARMONY
bis, il-lux-it no - Ms :
gen
tes, ve - ni
r
gen
et ad - or-
1
et ad -
et
ve-m-te gen
tes.
fir^
g i r j ' * 1
e fr
O 1
P \fQ
A?
IS^T
F-
- te, et
' r i
ad-or-a-te
v.
Do - mi - num,et ad
. m _ fj
or - a-te -
flti =
- or- a
1
1
\
et
ad
+p
i
- or
P
1
:
et
1
1
1
MODAL COUNTERPOINT
231
mi -
o '
et ad - or - a - te Do
mi - nnm:
5 hwi
fo o 1
prs f\
in
** qui
a
ho
di -
L_ _gJ
[.. "* I | fiM-- -]
e de-seen - dit Inx
lUfe 1 1 1 1 ! J ^-|- 1
de-seen - dit lux
M
-
| JJJ |
;
de-seen -
dit
, , 1
*V -,..5
"L. ^
, ,'* *-<&
* ~
1 1
qui
a ho
di - e
_ J _
i- r " i
i u i
w-f F [
mag - na in
jg,,
i i r i '
ter
if rl j '
ns,
1 _g m^-
de-seen - dit Inx
_ 1 = m+-
41 H
de-
^-4
seen - dit Inx
L r i
f
r j jji
i
de-seen -
^
I " * I
r p_[J 1 |, 1- j
de-seen - dit lux nag
s"~*+
s,
t
It
y
u
Haec
t-ft
1
1
a-
T=t
G
M uu-
Haec di - esquamf<
j & U JJk
bi_
3ci1
.Do
TT
-dit lux
mag -
W
|9
! r
Haec di
p e T^ T> 1
L =1H
1
T^-+
J_|_,_
J
na in ter - ris. Haec di - es
232
COUNTERPOINT AND HARMONY
1!
o
L^f p F f
i
Haec-
_ di -
- mi num,Hea
c
I IN |
-^ "
f m ? f
*):
Heao
di -
-F H J
esquamfecit
. , . u
Haec
di
66 qnam fe-cit
"J" - |
7- ~~P"]r i
"/|fc|p
-rn 3
T-
Hod f
ra '
'
-
es quam
J
cit
Do - i
ni
- num:
4*-^
Ex-
8Ul-
te - mus,
[
3E !7~~: I
_ 1
r -
1
1
| Ml |
'
|t=J
1
,i
Do
mi - num: Ex - sul - te - mus,
p
*ir
lae - te - mar ia e
ex - sul- te - mus, et lae-
^F=F
-te - mur in e - a, ex - sul- te - mus, et lae-te - mur
MODAL COUNTERPOINT
233
ry fc
-
a
!- Q -
L Q ^-
O '
rn 1
1
5
2-ff s
ex-sul - te - mus
_) 1 1 =q
et 1
ae- te - mur
in e -
a.
"IV
-4
tt-F
in e -
a
Exercise 12. Write a motet either to Latin or English words
founded upon Ex. 246 and Exercise 11.
Example 247, This is as typical of Byrd and the English School as
Ex. 246 was of Palestrina and the Italians. The melodic intervals,
generally speaking, are bigger and bolder. There is much more syncopa
tion. New features occur in the harmony. At bar 21 the tenor and
alto leap from" a discord. This progression is obviously derived from
the changing notes described in (165). But here the discord is never
resolved as it is in changing notes and the Nota Cambiata. Later
this figure became quite common. The close consecutives in bars
4-6, and 15-17 are not exceptional, nor is the imitation beginning
only one beat after the theme. Here the verbal accent is preserved
by the syncopation, but there are many cases where it is not. Never
theless the words sound to have the right stress if properly sung.
Observe the augmentation of the Alleluia theme in bars 23-25.
The following is a literal translation of the words :
Sacerdotes Domini incensum et panes qfferunt Deo
The priests of the Lord offered incense and bread to God
et ideo sancti erunt Deo suo et non polluent
and therefore they shall be holy to their Lord and shall not defile
nomen ejus
His name.
Ex. 247 Motet, 'Sacerdotes Domini'. Mixo-lydian mode.
Byrd.
1^ j=^
-TT ^y^^^^r^
TO a o- tfi
^ Sa cer -
f ^==g - J J
do - tes Do - - mi -
-e TB j-rr;
Sa - cer -
1
do - tes .Do - mi -
!-) J
Sa - cer -
do - te Do - - ' mi -
* O 3
A Sa
cer - do
tes
Do
mi -
234
COUNTERPOINT AND HARMONY
-ni in - cen - sum et pa - nes of - fe-runt De -
E
- ni in cen - sum et pa - nes of - fe-iunt De -
m
-ni in - cen - sum et pa - nes of - fe-runt De
^
A -ni
in - cen - sum et pa - nes
10
I I j I 1 _ 1 ^ .__
r
^-Tl
' r
\
'^
^
" M i =
et i de-o
-i
1
- f
S-
>t \
L -
H
de-
l=t
o sane -
J J i i J . t=i
- o, De
U:J J J =
o
et i
v^ Ji'~ r- m ~ \ m
de-o sane
,,,/ m m 2
A X fe-runt De
J lion
j
et i - de-
j J j j =\
** sane
InTr *
-A 1
9
~e
ti
e
i
-d 2
runt De-o
=H
9
1 1 i
ti e - r
ant
De -
8U
e r
o, De -
II nil ^
-ti
e -
runt
De -
su
-
o, De -
r f f M
j
f v
-
MI
sane
15
ti
i i
e - runt De-o
\
\
|
r^
8U
p^
f=l=
-
Tf=
Tirm pol -
1
f
pr
r j
- o
M
V
su
p=
'.'-
V
pnt
et
=1
non__
'-'- f
pol - lu-ent
-rr LJ__
-|
su
-
.o_
et non
& +
*
1 1
1
J
su
et
pol - lu-
MODAL COUNTERPOINT
235
^ . ,j ,
i d T-T-
- lu-ent no - men e
j ^ j p_p_
ius. Al-l-
If
!'l 1 "' 'I
no - men e - ius, no
men e - ins.
J 1 [Lnj i
pol - lu-ent no - n
t ?. , \ j j
4 * $**^ "
nen e - ius.
j
s
J t
^ r N- ==
- ent no - men e
5 20
/ f r o 1~
ius. Al-le-
l,i- . jj|
4
p-R ^ ^
- lu - ia, Al - le -
.!_. = p #F f 19
^ J I J I
lu - ia, Al-le-
,, rnrff tiu i
f
: i - r r i ' F
il-le - lu
a__= < p f 1 j ffr
-f M L1 -^ ^-
ia,, Al-le ia,
1- JJ Ff ^1
11 H H F
Al-le - lu
c f i r "
w . r i r ==
ia, Al-le -lu
J
A
J f
-lu - ia, ,'
' f~ |- Jj .
k-le - lu - ia,
2 P, , ,
-4-j 1
Tl
-lu I ia, AHe-lu
j f *r r r r ^r^ r- F=
-" o to I nen
- - ia.
r ^ * r r ^ A IL iJI
$
5f f ' F L -
Al -le-lu - ia, Al - le - lu
>^ i _ f^n^P^.. i =
-f 1|- [ 1 1 f r 1 Ml 1|
- ia, !A1 - le-lu -' ia.
lltr r r. r .,_ m^
' - 'ia, Al - le-lu - ia,^
-*^-- =^ --f * nr
J tL\L f. 9! Mi .
LI -le-lu - ia.
^Z 14. U. JJESJ 1 _
^ Al - le-lu - - - ia.
Exercise 13. Add the missing parts in the style of Ex.347
|ft r i 1 w I.V. -H^ . 1 I
ft
^ ^ "" ^U fi!
Sa - cer - do - tes
4
Do - - mi -
f
)
E5
li
^IA, e
2
s
Sa - cer - do tes
Do - mi -
236
COUNTERPOINT AND HARMONY
in - cen - sum et pa - nes of - fe - runt
in - cen -
me
-ni in
cen -
111 J j i i
| - J |
[1 J.. |
fo v. .r *h^
> De -
fir : J
o, et
7TT f-
i - de-o
|h i
^eti
Sane
R
f
et i - de
'
-H;
1 J , ,1 1
f
\ '
et
f^
i - de-o
IF?
FTh
|J J J ,. =|
*
ffi
H
i e
. , J -3
- runt
IP
I
31
)e
^
SU
ft*
m
h-
-
:*j
f
i
s
=1
j
s^=
aanc
\^
m
Pr
- o et
et
non
et
non
pol - lu-ent no -
MODAL COUNTERPOINT
237
=f
gr , I J==F
r r r J =^==
Al-le- In - '
ia,
|p lh =|
F
L_J 1
Al-le - In -
^r r r 1
Oi, " |p I
r r 4 r
Al-le -In -
^E=^=i
^s - men e
i i r r ff r r r i
ins. Al-le-ln
i
^ Al-le -
gJ
1
r ^
5
Al-le -
F-f
t v r _ _ _J!LA-
Al-le -
i i r i
Al-le -
-^ 1" 1 1
__JL 1 | 1 . .
41 Q
-ia,
Al-le - lu
ia, Al-le -In
4
^
la.
Exercise 14. Write a motet following Ex. 247 and Exercise 13.
The difficult imitations may be made easier by limiting the number of
voices taking part in them, and/or by lengthening the distance between
the entries of the voices.
SECTION XII.
THE THIRD SPECIES OF STRICT COUNTERPOINT.
Four notes against one. (Also three or six notes against one.)
163. The counterpoint usually begins on the second crotchet. It
may begin on the fourth, but only in combined counterpoint : that is
where other species than the first are combined with the third. No
part may enter on a discord, therefore the first note must be a harmony
note. In all bars except the first, "harmony notes must occur on the
first crotchet. The other three may or may not be harmony notes.
Generally speaking, it is smoother to make the third note a harmony
note, for when the student has to write more than one moving part
it is at the third crotchet, or second minim, that another part will
move, and dissonances will occur here if the third crotchet is not in
harmony with the C.F. Palestrina occasionally wrote these accented
passing notes, when the use of them improved the part progression.
The shorter the sound the less the passing discord is noticed. Examples
are given in Ex. 263, bars 1 (tenor), 3 (both parts), 5 (upper part) 7
(both parts), 10 (both parts), 12 (tenor) ; and in Ex. 264, bars 4 (both
parts), 6 (upper part), 10 (treble), 11 (alto).
164. The movement in this species, being quicker, must also be
smoother ; that is, more conjunct. The rules given in (29) must be
more strictly adhered to. As length gives stress (89, I), so quickness
should remove it. Nearly all that has been said in Section VI applies
here. The remarks on consecutives in (107) should be re-read. Ex. 248
shows consecutives in varying grades. Those marked with straight
lines should be avoided in strict counterpoint ; those with curved lines
are less audible ; those with dotted lines are harmless
165. Changing notes (Ex. 101 (d) and Ex. 249 (a) and (b)) are an
exception to the rule that a leap must not be made from a non-
harmony note. They are an example of contraction by elision (Ex. 250
(a) and (b) ). This occurs in music as in language. Its use may lead
either to carelessness or economy according to whether it is employed
badly or well. It will be seen that the first and last notes are the same
and must be harmony notes. The second and third are the two sounds
lying next above and below that harmony note. Changing notes are
most frequently used at the penultimate bar of a cadence They are
usually approached, and must be quitted, by step. If the second note
is above the first, changing notes should be quitted by ah upward
step ; if below, by a downward step (Ex. 251). They should be used
infrequently, for otherwise they clog the movement and hold it to one
pitch.
166. Two passing notes in the same direction must proceed in that
direction until they reach a harmony note. Ex, 252 (a) is wrong because
as D and E are passing notes, they should not turn back, but proceed
as at (b). Sometimes two chords in a bar obviate this difficulty as
THIRD SPECIES
Ex. 348
239
il , I r =q
II 1 1 J 1
Ir / J~ ,"1
_ 5 _
4 / r r
m~e
* *
|fj r J r 1
^^
_^
j!,l/
V
1 '
H /r r r
r ^ j j
-^
Ex.249
i j
I
J j ^
1
-J-
J [ ^ N
- tf o
1
1 _ 1
Ex 350
j j n\
$0 ^ 3
[) J J1J J
Ex.351
* "*
r '
J J J
" J
_
r r
Ex.353
TC==
1
tf f,
n H-J W * H
-5--"
Ex 253
A C-?
_JL ^
(1)
*
H-T>
o H
TTO
*J
f
m |-
f f f ,
|-
.pr
fe
t J JJ
p
"
km
()
=-* 1 | | 1 1 -J <
(2)
TV
4=
(8)
-O - n
, 11
AJ
p
!
=4:
a
F?4
F-
f*=l
p
-H
f-
.
r ff pf ^
(I).!
(a). A
-f-
wo cl
ccent
lord
ed j
s in a bar
>assing notes
-S-fH H
^. minor and
on the 3rd
F).
crotchet.
). Changing notes.
240
COUNTERPOINT AND HARMONY
in Ex. 263, bar 8, where the first chord is a triad on D. This would
make the C and B in the treble passing notes. But obviously the G
in the alto is an accented passing note leading to a change to a |.
167. The bass may leap to a second inversion as in 2nd species (106),
so long as it returns immediately to the note it left, or to the other note
of the same chord (Ex. 260, bars 7 and 9).
168. Tautophony must be avoided as in 2nd species ((105) (3)
Ex. 255). But repetitions occurring in the same bar (Ex. 255 (a))
hold up the flow of the counterpoint much more than repetitions spread
over two bars (Ex. 255 (b) ). The latter are harmless.
169. The interval of the tritone is ugly when it is found between the
highest and lowest notes of a passage (Ex. 256 (a)) ; but it is not notice
able when it occurs in the middle of an upward or downward scale
passage (Ex. 256 (b) and (c) ).
170. The 3rd species is designed for the study and practice of
passing notes ; therefore hopping about from one harmony note to
another, as shown in Ex. 257, is to be avoided as much as possible.
171. Some of the usual cadences are given in Ex. 258, and in the
working of the C.F.s which follow.
172. The student may now work examples, first in two parts, then
in three and four. Par. (108) should first be re-read.
173. The examples of combined counterpoint given in Exs. 263
and 264 are very difficult and of very little practical use. They are
inserted here for the sake of completeness and to exemplify (163) and
(166).
N.B. No C.F.s are supplied for exercises in this section or in the
next. Those given in previous sections can be used for this purpose.
Ex.254
m
C.F.
K i J i J j
i i j j i
FP~? i
j , PP i
py P p i
1 i*"
rTi
i n
ii) y tf j w j
i n
^N-t
o
o
Ex.255
THIRD SPECIES
241
Ex.256
(ft] IJ J J
(i) 1
J llf IJ J J J
(c)
J J J 1 i* 1
Ex 257
g
Ex.258
IJP Jjjjl
o
[Jj J Jl
m ft *
y"
U
1^
U
[-8
XX
*"
^
Ex.259
ii it r i
\ ^
iipiii ^ r J J
T*
m m M
r^
J - J I
H i 1 H
-e
J J J p
h-^
L r . J
IRS * ? *
'' : l o
W4=
*>
i j r J J
J J J J
^ * * r
rrr J
nrrif I 1
- ,
p P * p
f-
i r
"* p F ^
IT" -
NH
M
i' ' r r
R
242
COUNTERPOINT AND HARMONY
Ex.260
2
3
4
5
6 "
C.F
PiU "
TI
-n
-n
frK-
(
Jj ij
1 P ,1*1. Ilil
8
9
pO
rr rr
10
p^
11
^^ J J
12
tJ
^-^i
Kl.
^
4 2
^^
If^p
i
5^
JyiH
~o
Ex. 361
Zuversicht 3
C.F.
C.F.
I
^
p
THIRD SPECIES
248
C.F.
C.F,
it
33=
Ex.6
244
Ex.363
1
COUNTERPOINT AND HARMONY
2 .3 .4.
\i * \\ i J r J Jl ' ' ' ' ' J I-"'*"-' I' '-I I I"'"'-
Ifi I
^.B j e ci [ - -m -
4 J * '
r p r
Mil*'
|r r r
- * r
C.F.
i i
p 1 i
6
8
ijH fFpj.J^
Jill 1
j J I j i i
i 1
ftp r r *
* * J j
f . r I
j j j
*Jt> =
-F ^ eT
' f r
L-S OL- , _,J I
9
[1* JJ JJ J .M
10
n
12
13
m ^
r j^ rr
P ',>
rr j rr j
LJ _r r I
jf
J^y "-=
|( I f I
i-i- i i
=
Ex.264
[J^ ]
riJJJ'
I I .rfr-
| 8 . IJj.rl
4
-*-
cfe:
ffi J J
* J rr rr
r j JJ rr
-I-
-J-F-
C.R
-^
~^=
TT
6
^
g
THIRD SPECIES
10 11
245
12
13
SECTION XIII.
THE FIFTH SPECIES OF STRICT COUNTERPOINT.
174. The 5th species of strict counterpoint, often called Florid
Counterpoint, is a combination of the other four species with the
addition of occasional quavers. The rules for the first four species
apply to the fifth, together with the following :
(1) Only two consecutive conjunct quavers may be used, either at
the second or fourth quarters of the bar. They must be
approached and quitted by step.
(2) The semibreve must only be used in the last bar except when
there are sufficient moving parts to maintain the interest.
A semibreve thus used must invariably be tied to justify
its weight. Preferably it should be the preparation of a
suspension. There should be at least two or three moving
parts, therefore semibreves cannot be written in counter
point of less than four parts, and even then should appear
infrequently. In .five-part counterpoint they are used
more freely.
(8) A dotted minim also holds up the flow, but to a less extent.
It should not be used in two-part counterpoint, and not in
three- or four-part unless there is at least one other moving
part.
(4) Minims may be used freely, but when the weight is thrown
on to the weak half of the bar by writing a minim preceded
by two crotchets, or by a crotchet and two quavers, the
minim should be tied to justify its weight.
(5) Suspensions are resolved plainly, or by either of the ornamental
resolutions given in Exs. 197 (b) and 200. Occasionally
the type of resolution shown in Ex. 197 (b) may be
modified by using crotchets instead of quavers. This
produces an accented passing note at the third crotchet,
and may result in some awkward clashes. The suspensions
described in (135) may be used, but they are of course
impossible when the C.F. is in the lowest part.
(6) Parts must not enter at the beginning of a bar.
(7) No part may enter on a discord.
(8) When there are three parts in florid counterpoint there should
be movement in some part, or parts, on every crotchet in
every bar except the first and last, and on nearly every
crotchet when two parts are florid. Movement should not
be confined to one part, but should be distributed equally.
The same rhythm should not often appear in the same part
in two consecutive bars.
(9) Rests may be used to heighten the effect of a point of imitation,
not to get out of difficulties. It is not wise to use them in
less than four-part counterpoint.
FIFTH SPECIES
247
175. The above rules require some amplification. It will be noticed
that the first four are concerned with limiting the use of rhythmic
patterns in order that all light and quick notes may occur at light
and unaccented divisions of the bar, and all heavier and slower ones
at heavy and accented divisions. Where long notes are used at the
weak half of the bar they must be tied over the following accent to
give them due force, except when they are preceded by notes of their
own length. No minims are used at the second quarter of any bar.
These rules have the effect of stiffening and conventionalising the
music by making the bar accent very rigid and prominent. Like all
conventions, 5th species is easy to learn and abide by, and originated
in the " safety first " theory. But it is useful in teaching the beginner,
for it cannot lead either to rhythmic chaos or inertia. The licentious
are curbed by it, and the lethargic are obliged to bestir themselves.
In Victorian times it was practised ad nauseam for examinations. This
was partly the cause of the enormous output of innocuous and
plagiaristic cantatas, anthems, services and the like, so characteristic
of those days. A little of it can do no harm, but only as an introduc
tion to the greater freedom and imaginative quality of real XVIth
century counterpoint.
176. Ex. 265 shows all the possible sub-divisions of a bar in 5th
species, exclusive of those where the first note is tied to the last note
of the preceding bar. As the first note may be thus tied in every case
except Nos. 1, 3 and 4, there are in all 23 available rhythms.
Ex.265
1 2345 6 7
177. Imitations make this species of counterpoint much more
interesting if they are written smoothly. The varied rhythms make
this considerably easier than in the former species, both as regards
the invention of rhythmic figures to imitate, and the regulation of the
movement of the parts not concerned in the imitation to avoid clashing.
Practice alone can give facility ; but it will be found that when the
notes at the third quarter of the bar are consonant with the C.F.
imitation becomes much easier (163).
Ex. 866 Imitations and Sequences are shown by square brackets
248 COUNTERPOINT AND HARMONY
Ex.267 "
.GR r
^ r >x ^~>
r r r if
3X1
Ex.268
Ex.269
"TT~
ZZ=
FIFTH SPECIES
249
Ex.370
Ffr^
I
4 fc =
N_
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i p * m p
TTl
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1
J fL.
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M r*rn
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^
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o |
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C.F.
PP^
COUNTERPOINT AND HARMONY
Ex.373
C.F.,
FIFTH SPECIES
251
Ex. 374
err rn
m
r-j p-t-
1 *y-i
ill ' '""I
$* " J
b^^
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^ JJ
1 ^
| 1
r- j-
iJJrH
4-H
yjfar
C.P.
df~
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1 r 1
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v J Ji
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r-=-="
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p
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(1) The augmented 5th in such a slight discord that there is no
harm in entering the Alto at this point.
Ex.875
r-fl
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ii...,
The wide compass of the Soprano and the stop for four crotchets
on the double suspension seem to be justified by the sequential building
up to the climax. There are two chords and a suspension on the third
crotchet in the penultimate bar.
COUNTERPOINT AND HARMONY
The tenor and Bass are in Canon.
(1) The Tenor enters on a 4, but the dissonance is slight and
only lasts for one crotchet.
(2) There are two chords in this bar. It is better not to allow any
part to cross the Bass as a rule, but this is harmless ; the
E in the Tenor sounding like a passing-note in the Bass.
(3) Two chords in the bar.
(1) See (124 (5)) and Exs. 163 (/) and fe).
Ex.378
,C.F.
FIFTH SPECIES
253
(2) ~ (1)
() (1)
(1) Two chords in a bar.
(2) Suspensions of the type shown in Ex. 203 (6).
.. This shows how a chorale or hymn-tone may take the place of the
ordinary C.P. The form is that of a choral prelude with short interludes be
tween each phrase of the tune. The themes for imitation may be either found
ed on the phrases of the tune, like (a) and (c) or independent of it, like ft).
Tune by S.Howard (1710-1782;
254
COUNTERPOINT AND HARMONY
Egi
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r fa)
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(2)
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(9)
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(5)
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(7)
FIFTH SPECIES
255
jPfy f frj-
ufj ,1 J
, i4--s=a*^
8:
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e
(1) A crotchet tied to a crotchet is permissible, but not a crotchet
tied to a longer note.
(2) Rather low, but as it is only touched on an unaccented part of
the bar, the imitation justifies it.
(3) The A is an unessential note. Both the 5ths are unaccented.
(4) Suspension of the type shown in Ex. 203 (&).
(5) The quavers might be taken as two passing-notes in the same
direction not proceeding to a harmony-note, but as there is no dissonance
this would be pedantic (166).
(6) The Alto enters on a discord with the Bass, but only a
slight one.
(7) Rather too many consecutive minims !
PART II.
DIATONIC DISCORDS
i
SECTION XIV
THE SECOND INVERSION OF TRIADS AND THE CHORD
OF THE DOMINANT SEVENTH AND ITS INVERSIONS.
178. The two chords treated of in this section are both rather pale
and characterless-musical pawns, in fact. They have their uses
but have little importance of their own and do not affect the emotional
feeling.
The Second Inversion.
179. The first, the J chord, is usually learnt along with the , and
treated as the progeny of the triad equally with the first inversion
But it will be seen from what follows that there is only one use of it
in which it sounds to have any relationship to its parent triad. With
that use the student has already been famihansed in (106), (167), and
Ex. 226. It now remains for him thoroughly to get hold of the two
other uses. , . . , . , . ,
180. The more important of these is what has been termed the
Cadential Six-four, because it is often not always used at a cadence.
It sprang from the appoggiatura, or " leaning note. This is simply
the note either a whole tone or semitone above * or a semitone below
any harmony note, approached by leap and Mowed immediately b y
the harmony note. If approached by step, as in Ex. 283 (b), bars 2
and 3, it is strictly speaking an accented passing note. Appoggiaturas
were first written' in small type. As early as Bach's time they were
written both ways (Exs. 280 and 281). In the end it was found in
convenient to write them as small notes not accounted for in the length
of the bar, for if written thus they did not clearly indicate the com
poser's intention) In the late XVIIIth and early XlXth centuries
these and all other ornamental devices were extremely common ; and
it was then that the cadential * flourished, every type of music abounding
in examples.
* The lower note must have a strong tendency to nse. If it w a semitone below it acts
as * leading note. There are occasions when tt mil nse logically even tf tf a whole
tone below the following harmony note.
Ex. S80
SECOND INVERSIONS 257
W Bach. St. Matthew Passion
. >fj-
181. Its construction is clearly shown in Exs. 282 and 283. It
will be seen that the note above the 5th and 3rd of each triad is sounded
first and then allowed to drop one step to its resolution. Strictly
speaking the B flat in the treble of Ex. 282 (b) (1) is an accented passing
note, and the D in the tenor an appoggiatura. At (2) this is reversed,'
the treble leaps and the tenor moves by step. In Ex. 283 (b) the 6
at (1) is strictly a double suspension, as both B flat and D are prepared.
But these are merely accidents, for the cadential J may be used freely
all three ways by leap, by step, or with a preparation of one or both
notes.
first phrase of tune ly H. Carey
258
DIATONIC DISCORDS
182. As all musical ornaments of this type occur before and not
after the notes they decorate, it stands to reason that a cadential *
must occur on a more accented note than its resolution.
183. The usual rule with regard to its approach is as follows :
" The bass may only leap to a J if it does so from the root of another
chord, or from another inversion of the same chord. If it approaches
from the inversion of another chord it must do so by step." This is
difficult to remember and the reason for it does not seem clear. But
if the * is regarded as two appoggiaturas, then all that has to be
remembered is quite obvious, namely, that if the triad used is
appropriate, it will still be appropriate when decorated by the
appoggiaturas. Likewise if it is inappropriate and does not sound
well without appoggiaturas, it will be just as ugly with them. Ex. 284 (a),
(b) and (c) shows the only possible cases of a bass leap to the triad on
G from first inversions of other triads, for the bass will move by step
from the 1st inversions of the triads of D minor and F major. (The
1st inversion of the chord of C would not have controverted this rule.)
Ex. 284 (d) 9 (e) and (/) shows the same progressions with * chords, or
appoggiaturas. It will be seen that (a), (b) and (c) are ugly, (a) because
of the poor relationship of the triads of A minor and G (21), and (b)
and (c) because they contain too many common notes (70).
" ar
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li
;
j<j
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r/).
184. There is also a rule about quitting a J : " The bass must either
remain until the * is resolved, or else quit it by step." This rule is
also needless if the * be regarded as two appoggiaturas. For if there
had been no appoggiaturas the bass would either move when the rest
of the parts moved, or it might have one or two passing notes as in
Ex. 285 (a) and (b).
85
^ A
SECOND INVERSIONS
259
185. An exceptional treatment of the * is given in Ex, 286 where
the 4th is fesolved upwards and the 6th allowed to leap. A still more
exceptional treatment is shown in Ex. 287. Here both parts leap.
The explanation of these is that nowadays one feels there is so little
dissonance in a J, as its sound has become so common and ordinary,
that, provided it is followed by a | on the same bass note, the resolution
need not always be strict in order to sound well.
Ex. S86 Ex. 287
186. The other order of J, the Passing Six-four, has even less
importance and distinctive colour. It first occurred when passing
notes between two more important chords happened to make a 2nd
inversion. As with the previous kind, the modern usage of it is freer.
No doubt at one time all the parts always moved by step or
sustained a harmony-note from the previous chord and thus
the chord had no separate existence. But to our ears passing *s
sound well enough if the bass approaches and quits them by step and
the other parts move smoothly. They are, of course, most often used
at less accented parts of the bar than the chords which precede and
follow them. Ex. 288 gives all three varieties. Cadential *s are
marked (1), passing *s (2), and those which occur when moving through
the different positions of the same triad, or when the bass jumps to
the 5th of a triad and then : returns, are marked (3). The passing Js in
bar 1 are normal. In the one marked (a) the 6th, G, is used as a pre
paration for a suspension ; (b) and (c) are consecutive (see below).
At (d) the tenor skips, but both tenor and alto are really anticipatory
notes ((133), Ex. 197 (d)). At (e) the tenor leaps in quitting, and at
(/) both alto and tenor leap in approaching and quitting, and treble
in approaching. This is quite a fresh and jolly-sounding passing J. At
(g) the cadential J is not quite normal, for the 4th is doubled, but both
alto and tenor quit it by step, thus satisfying any feeling for resolution.
The last example at (h) is fairly common at the final cadence. Here
the leading note descends, but by step.
Ex. 288
)
w
rm^
J j.
200
tj- fP
\L ^. m m m ft
DIATONIC DISCORDS
J Vf-M' , (S) . (A)
r rr
-
r r
*
187. Obviously two cadential Js cannot be consecutive, but a
passing * may be followed by a cadential one (Ex. 288 at (fr)), or two
passing *s can follow each other (Ex. 289). The text-book rule is
that in this case there must not be consecutive fourths with the bass,
as this may sound crude (Ex. 290). But a string of passing *s, with
consecutive 4ths, as in Ex. 291, can be made to sound quite beauti
ful. They are best in three parts, the tenor in this example having to
dodge about until the end of the bar.
Ex. 28d
^
Ex. 390
Ex. 391
The Dominant Seventh.
188. The study of this chord follows naturally upon that of the *,
for it is of the same order an unprepared discord of the mildest type,
with just a little more pungency than the j.
189. The Dominant Seventh is resolved either by descending one
step with a change of chord, or by remaining stationary whilst the chord
changes (122). As its name implies, it has the fifth of the scale for
its root, and consists of the dominant triad together with a minor
seventh from the root. It is another example of contraction by elision
(165), for it first appeared as a passing note (Ex. 292 (a)). It also
appeared as in Ex. 293 (a), where it is prepared, before it was taken
without preparation. To use it as a separate chord, therefore, as in
Exs. 292 (b) and 293 (5), was not after all such a great innovation.
DOMINANT SEVENTHS
Ex. 393
261
Ex.S
^
J9S
J r^-n,
fl r
A
~T
ZL_
^
1
190. Students who have worked conscientiously and thoroughly
through this book up to this point are not likely to fall into the errors
which are common enough in the work of those who are plunged into
dominant 7ths in four parts after they have done a few exercises
in triads and their inversions. They have already learnt from
Section VIII that discords usually resolve by descending one step and
are not likely to resolve a dominant seventh as at Ex. 294. They
have a complete knowledge of the treatment of the leading note, both
in regard to doubling ((23) and (98) etc.), and also as to its progression
((52) etc.). Such sounds as' those given in Ex. 295, therefore, will
surely not be heard in their work. They are familiar with the bad effect
obtained by some part moving by similar motion to the note on which
a discord resolves ((116) (3), Ex. 146), and their ears will naturally rebel
at the resolution of the Dominant 7th shown in Ex. 296.
Ex.394 Ex.95 Ex.S96
Hr
191. The common resolutions of the Dominant Seventh are those
given in Ex. 292 (b) and Ex. 293 (6), where the chord is followed by the
triad on either the tonic or the sub-mediant, the 7th descending one step
and the leading note ascending one step. There are four sounds in
the Dominant 7th, and only three in a triad. This, together with
the arbitrary movement of 7th and leading note, makes it impossible
to get full chords in both harmonies when the Dominant Seventh
is followed by the tonic triad. In this case three notes in the
Seventh move arbitrarily ; only the 5th is free to move and yet cannot
go to the 5th of the tonic triad, for that would make consecutive fifths.
At Ex. 292 (b) the tonic triad is incomplete ; but generally speaking, a
more satisfying effect is obtained by omitting either the 3rd of the
dominant 7th (Ex. 297 (a)), or the 5th (Ex. 297 (6)), the doubling of the
262
DIATONIC DISCORDS
root thus enabling one part to remain and form the th of the tonic
triad. The reason for this is that the tonic triad usually occurs at a
moment of greater stress and has a longer duration than the 7th which,
being itself an essentially weak chord, is more appropriate at a weaker
part of the rhythm. Ea'ch case settles itself by the progression of the
parts.
Ex. 397
(i)
Ex. S98
>4
^
8
il
""" Oil
JX
n
^
^ZL
U
192. Another resolution is shown at Ex. 298, where the 7th does
not descend, but remains to form part of the next chord. The resolu
tion of the 7th may be delayed (Ex. 299), if this is made quite clear by
giving it an important enough position rhythmically. Its resolution
may also be transferred to another part (Ex. 300), but it is not customary
to do this when the two parts concerned make a 7th followed by a 9th
(Ex. 301). These last two methods of resolution can be applied to
discords other than the 7th.
Ex. 299
Ex. 800
'=*=
Ex. 801
i
The Inversions of the Dominant Seventh.
193. As chords of the 7th contain four notes, they have three
inversions, s, 4, 4. Unless it is necessary to show some special part
progression, or unless some note requires an accidental, these figures
are abbreviated to J, J, The chord in its original position is figured 7.
194. The first inversion of a Dominant Seventh has very much the
same relationship to the chord in its original position as the first in
version of the Dominant triad has to the triad itself. Where a Dominant
triad can be used, a dominant 7th can also be used, and where the 1st
inversion of the triad would be fitting, it is possible to employ the
1st inversion of the 7th, provided that the following chord resolves the
discord. The use, however, of sevenths and their 1st inversions at
every possible opportunity instead of triads and their 1st inversions
undoubtedly weakens the harmony. No hard and fast rule can be given,
but generally speaking, it is better to reserve the discords for places
DOMINANT SEVENTHS
263
where they can be passed through smoothly at unimportant rhythmic
points. If the concord has been used on the important beat the discord
will always follow it well. There are few places where this discord
sounds well at the end of a phrase, even though the first chord of the
next phrase resolves it. It is best used as a passing chord between the
last chord of one phrase and the first of the next. In Ex. 302, (a) shows
a weak use of the dominant seventh and its inversions, whilst (/;) con
forms to what has just been said.
Ex. 303
w,
8 7
66
5
7 6
766 5687
1! 4 - 3 -
The very weak chords are marked with asterisks. At bar 7 in (b) the appear
ance of the 7th is delayed to the last quaver in the bar, and then it only ap
pears as a passing-note.
The First Inversion.
195. The common resolutions of the first inversion are given in
Ex. 303 : (a) shows the resolution on the tonic triad, (b) on the sub-
mediant, and (c) gives the resolution in which the dissonance remains
to be part of the next chord. The resolutions in (c) should not be
confused with those in Ex. 303 (d\ which are merely delayed resolutions,
the dissonance eventually descending, not remaining. The leading
note always rises, except when the dissonance remains : if it did not,
a diminished 5th would be followed by a perfect 5th between the
dissonance and the bass, as at (e) see (102 (4)) and (127). Dis
sonances between the bass and any other part are always heard more
strongly than those between upper parts.
Ex. 803
Jr o n
j , \
j-e n \
* i
I * j >
Sg! u _e
ii
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V
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e **
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r T
LLA
264
DIATONIC DISCORDS
(4
The Second Inversion.
196. The second inversion bears a strong likeness fo two other
chords the passing * and the first inversion of the diminished triad
on the leading note. Ex. 304 (a), (b) and (c) gives three progressions
which are the same except for the middle chord: (a) has a passing J, (b)
a chord of the sixth, and (c) the second inversion of a dominant seventh.
The passing * and the 4 do not give such a good part-progression as
does the *. Handel invariably used the latter in the cadence given in
Ex* 305 which he must have written hundreds of time. The student
should train his ear to recognise the slight differences of harmonic
colour in Ex. 304 and similar progressions. Even such a well-Jaiown
musician as Robert Franz evidently did not appreciate them for, when
he wrote his additional accompaniments to " Messiah," he converted
many of Handel's Js into *s, thus giving the music a very un-Handelian
flavour. The similarity of the J and the 4 has probably given birth
to the peculiar resolution of the latter shown in Ex. 306 where the dis
sonance rises instead of falls (Ex. 95). As a rule it follows the move
ment of the bass, as in Ex. 307. Certainly it never rises when the
bass falls, as in Ex. 308. It is essentially a passing chord. The bass
must approach and quit it by step, and the other parts should move
smoothly through it as in the case of a passing J.
Ex. 304
(
^
^fa
Ex. 805
J .1 J
Ex. 306
Ex. 307
Ex. 808
4_u s
ji a H
j.
r f f
J j i
r|
f
r -p
T r r i
DOMINANT SEVENTHS
The Third Inversion.
265
197. The last inversion is the strongest, for here the bass has the
dissonance (Ex. 309 (a) and (b)). It does not resolve on the sub-
mediant chord as often as do the other positions, for this results in a J
which is not always a fitting chord. Ex, 310 (a) and (b) 9 however, is
harmless enough.
Ex. 309
A ()
~
Ex. 31C
>
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i-
il.
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Ex.811. Version I, is a simplified harmonization of the chorale given in Ex
ercise 4, Section T. It offers many opportunities for passing ^'s, but shows
how weak these chords are, and how often they cause one part to stand still.
The dominant seventh in the penultimate bar is sustained too long and arrives
at a point in the bar which is too strong for it. The cadential s in bars 10
and 13 are weak.
NNHn
T
J. J J 1
~t i 1
IJ ] j 1
yi H
r r r
J j j
L2 ^_J
r r r
,) J J
ihH=
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6ft-)
r r r '
ecp)
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'f r r '
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ji
r r
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o * *
a*
-i si ^
r r r
rT T
a
r ^
B f
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6(P)
(
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f r
u C/
J
o
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6(0 l
&
we
Op)
k
li
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266
DIATONIC DISCORDS
In version II triads and their first inversions are substituted for most of
the |'s.
rf'
frr
fc
m
Jj
^^^i
Version IE employs all the resources made available up to this point. Note
the accented passing-notes in bars 7, 13 and 18, and the double suspension in
bar 16. Compare the latter with the in version I.
DOMINANT SEVENTHS
Exercises on Section XIV.
267
1 Add Alto and Tenor.
r
f
m
m
4 6
3
643 6
6 646-
5 8
wm
! 4 6 4 6 5|456 7
3 2 tj5 8 4
659 876 657 1
. Add Alto and Tenor to both versions and compare them.
Chorale, 'Liebster Jesu*
76893
34 5
rH i-il
"i n n i 1
$ J J J =
1 J
J d
' ^
SE
464
i 43
| ^ g
65 8387
548-
N
6
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5
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1-7
1
j -
268 DIATONIC DISCORDS
8. Add Alto and Tenor.
886 6 5 jf
* 8
6 6 6 . ^
*I*
5-5656 6 -
3 - 3 h4 3 8
m
. ^ ...
PP^g
r rrJ J U
47 - 6 6 8 7873483k 87 # -
64
8
6 7
5
4. Add the three lower parts to N9? 4, 5 and 6. Cadential ^s are indicated
by (1); passing ^'s by (2); the dominant seventh or one of its inversions by (8).
'In dulci JubilJ
ilii I r r ir rr JM J i nr II
(i)
(2) (2)
(1)
i^
r <' J i
(1) (8)
(1) (8)
i r r r. i "is
(8)
5.
^
(2)
I to D min.
J IJ J |J'J
(8)
(2) (1) (8)
'toC
p t p 1
Ff=l
rs r
p 1
i i i
*
8)
4
; r ir i
(8) (3)
f f-
t LJ
(8)
1 u
- '
DOMINANT SEVENTHS
269
6.
Irish
i
UnCmin,
m
(3) (8)
(3)
r r ir r
(3)
(3)
to)'
(i)
Any of the melodies previously given may now be rebaxmonized using se
cond inversions of triads and dominant sevenths with their inversions.
7. Add the three upper parts to Nf 7, S and 9. Supply the harmonies where
the bass is unfigured.
fF=f
=t=
6
4
5
8
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65
48
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66
54
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8-
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270
DIATONIC DISCORDS
SECTION XV.
THE CHORDS OF THE NINTH, ELEVENTH AND
THIRTEENTH.
198. The chords of the ninth, eleventh and thirteenth are
selections of notes from the complete dominant discords given in
Ex. 312 (a) and (b). These contain all the notes of the scale, but they
are never heard simultaneously, for they would make a very strong
dissonance, and seven parts would be necessary.
Ex. 313
(a) Major
\l aP\\ 4
(b) Minor
ft V;u
i 3 n
R
*
199. It is not difficult to understand how the unprepared discords
of the ninth, eleventh and thirteenth came into common use, for as
soon as musicians became accustomed to the sound of one discord
taken without preparation (the dominant seventh) they would naturally
try the effect of others of a more dissonant character.
200. The strong relationship of the dominant and tonic triads
(20, etc.), the great attraction which the perfect cadence has had for
composers since the XVIth century (41), and the invention of the pedal-
point (136), no doubt partly accounted for the use of the fundamental
discords as they were called. Probably, also, as in the case of the
suspension, the mistakes of executants, who hit the note above or
below the one they were expected to perform, suggested the appog-
giaturas. The dissonant notes occurring in many ninths, elevenths
and thirteenths comply with the definition of appoggiaturas given in
(180), and where they do so they can be regarded as such. The earliest,
clumsy organ pedal-boards must have encouraged organists to try the
effect of one bass note held beneath a change of harmonies above.
Instruments with a drone-bass had a similar effect, for their drones
sounded the first and fifth notes of the scales. In Ex. 813 the appog
giaturas, or dominant discords, all resolve on some position of the
dominant seventh. The seventh itself is resolved only twice, once in
the soprano in the second bar, and once in the alto in bar 3. The
whole passage is upon a dominant pedal and is nothing more than an
elaborated perfect cadence.
NINTH, ELEVENTH AND THIRTEENTH 271
Ex. 313
m
201. Until towards the close of the XlXth century the chords of the
9th, llth and 13th were built solely upon dominant, supertonic or tonic
sevenths, all of which had major 3rds, perfect 5ths and minor 7ths.
Those on the supertonic and tonic are therefore chromatic (Ex. 314)
and will not be considered until later.
Ex. 314
^ Super-tonic
Tonic
tF k-
1 ** r** 1
^
tl
202. These discords were resolved either with or without a chord-
change (189). The degree of dissonance, the position of the dissonant
notes in the scale, and the movement of the parts determined the
question as to whether the discords fell one step, rose one step, remained
where they were, or, in the case of the thirteenth, fell a 3rd to resolve,
(Ex. 315).
Ex. 315
(a) Bom. ninths ($) ( c )
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272
DIATONIC DISCORDS
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Dom. thirteenths
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203. In modern music the use of these chords is much less restricted.
The revival of the modes brought with it a freer use of triads, and a
freer use of discords founded on these triads followed naturally. The
strongest relationship between two triads is that between dominant
and tonic : that is, between two major triads the roots of which lie
a 5th or 4th apart. But there is also a relationship between any two
triads the same distance apart, even if both are not major. The
sequence in Ex. 316 (a) contains nearly all the possible combinations
of triads a 5th or 4th apart, i.e., major^major, minor-major and minor-
minor, the only missing one being the minor perfect cadence a major
triad followed by a minor. At (b) the same sequence is given, but
each chord except the first and last is a prepared seventh. This only
presents one new feature the resolution of one discord on another.
Bach's Prelude and Fugue in D major for the organ is an example of
such strings of sevenths, but they are common enough. At (c) the
same sevenths are taken without preparation and still sound quite
normal to modern ears, even though the resolutions are delayed as
indicated by the dotted lines. At (d) some are i>ot resolved except by
the chord progression. There are also consecutive! 5ths and consecutive
discords. The former sound well here because the discords distract
the ear from them. The student should carefully compare all four
passages, but he must not write progressions similar to the one given
at (d) until he composes, and then only when they are the spontaneous
outcome of his musical thought and feelings.
THE NINTH
273
Ex. 816
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The chord of the Ninth and its Inversions.
204. Unprepared ninths are now used on practically every note of
the scale. Their dissonance varies according to the intervals of which
they are composed, the intervals between the bass and the other notes
being more important than those between the upper notes themselves.
Those having minor 9ths (i.e., the ninths on the mediant and leading-
note of major scales, and the supertonic, dominant and leading-note
of minor scales) are more dissonant than those which have minor 7ths.
The diminished 5th in the ninths on the leading note of both major
and minor scales adds to the dissonance of these chords. There is
also the 7th to consider which lies between the 3rd and the 9th, and the
fifths between the 3rd and the 7th and the 5th and the 9th. The degree
of dissonance can be worked out in each one if wished, but the ear
should be the best guide. The dominant major ninth is the least dis
sonant for it has no minor 9th or major 7th, and its diminished 5th
does not lie between the bass and another part, but between the 3rd
and the 7th. Next to it come the ninths on the supertonic and sub-
mediant (no minor 9th or major 7th with the bass, and no diminished
5th) ; then those on tonic and subdominant (major 7th with the bass) ;
274
DIATONIC DISCORDS
finally, the most dissonant those on the mediant (minor 9th with
the bass, diminished 5th between 5th and 9th) and the leading note
(minor 9th and diminished 5th with bass). These can all be sampled
in the sequence given in Ex. 317. All discords sound much smoother
in a sequence than they do when isolated ; and even the resolution of
the subdominant 9th on the diminished triad on the leading note in
this example is quite tolerable.
Ex. 317
m
a^
A
The Dominant Ninth.
205. The dominant ninth, being the smoothest, will be considered
first. It resolves either whilst the rest of the chord remains, leaving a
dominant seventh (Ex. 315 (a)), or straight on to the tonic chord
(Ex. 315 (&)). The 9th commonly resolves by falling one step as an
appoggiatura, or on to the 3rd of the dominant chord, as in Ex. 315 (c),
in w r hich case it either rises one step or falls a 7th, as at (d). The
dominant 7th is not always present in the chord of the ninth (Ex. 315 (e) 9
but if it is it should be resolved. A common procedure is that given
in Ex. 318 in which the extreme parts make a 9th, 7th and diminished
5th in succession. The contrary motion by step makes the effect good.
One has become so acclimatised to the progression in Ex. 319 that the
alternative bass given below presents no terrors to the ear, although it
moves in consecutive 9ths with the upper part.
Ex.318
Ex. 319
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206. The most common resolutions of the inversions are given in
Ex. 320. The root is often omitted in these inversions. When it is
present in four-part writing it excludes one of the other notes, usually
either the 3rd or 5th. As in the case of the other dominant discords the
part-progression settles the question as to which note is left out. In
Ex. 320 (6), although the alto proceeds by similar motion to the note
upon which the discord resolves, there is no bad effect. If the alto
rises to a unison (Ex. 320 (c)) the chord becomes thinner.
THE NINTH
275
Ex. 320 (1st Inv.)
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207. The older harmony books did not permit the major ninth to
be heard below the third of the chord, but this is now unobjectionable.
208. The second inversion follows the same rule as the second in
version of a dominant seventh. The bass quits it by step, and the 7th
rises or falls a step according to the movement of the bass (Ex. 321).
Ex. 321 (2nd Inv.)
-ft:
209. The dominant minor ninth is resolved in the same way as the
major ninth. If the A's and E's in the previous examples are flattened,
it will be found that they sound equally well in the minor, including
those which will involve the use of the augmented 2nd.
210. The first inversion of a dominant minor ninth forms the chord
of the diminished seventh. This has many resolutions besides the
ones given in Ex. 320, for it has a peculiarity only to be found in one
other chord the augmented triad. In each of these chords the notes
are an equal distance apart ; those of the diminished seventh are a
minor 3rd, and those of the augmented triad a major 3rd above each
other. Thus; in the augmented triad, by enharmonic change, every note
may be either the 3rd, 5th or 7th of the scale (Ex. 324). Similarly
in the case of the diminished seventh, every note may be either the 7th,
2nd, 4th or 6th of the scale (Ex. 325 (a)). Ex. 325 (b), (c), (d), (*)
shows the effect of modulation by the somewhat cheap and easy method
of enharmonically changing the notes of the diminished seventh.
Ex. 322 (3rd Inv,)
Ex. 333 {4th Inv.)
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276
DIATONIC DISCORDS
Ex. 834
A min.
003
Fmin.
Cfmin.
Ex. 335
U).
211. In Ex. 326 all the ninths can be regarded as appoggiaturas,
except those at (a) (combined with a suspension), and (b) (tenor and
soprano). At (c) the alto and bass are passing notes, even though they
leap to the appoggiaturas at (d).
THE NINTH
277
Ex. 386
f A lawyer te went out one day{ English Folk Song.
(Copyright)
Some of the following exercises are for pianoforte, as it is not
a good thing to write exclusively for voices. The work of many
English composers has suffered through this practice. At first it is
necessary for the reason stated in (27), for the voice is limited in compass
and comparatively slow in movement. To allow unlimited compass
in the part- writing and to ask a beginner to write quick passages would'
only be distracting. But a stage should now have been reached when
a little more freedom will be advantageous inasmuch as it will prevent
the student from thinking perpetually in the same idiom. Piano music
need not always be in the same number of parts throughout an exercise,
but care should be taken over the progression of each part as in the
case of vocal music. Leaps of larger intervals than have hitherto been
used, or of augmented and diminished intervals, may now be written,
as well as arpeggios. The notes to be played by the R.H. should be
in the upper stave, and those for L.H. in the lower, unless it is more
convenient to write them otherwise, when the mark " R.H r " or " L.H."
should be inserted. When any part proceeds from one stave to another
a straight line should be put in to show where this occurs, as in Ex. 327.
Ex.327 (For Piano)
Minuet (a)
278
DIATONIC DISCORDS
Ex. 327 begins with a tonic pedal, so that the chord at (a) is the
first inversion of the dominant ninth ; at (6) the second inversion of
the ninth is combined with a suspension, and at (c) the third inversion
with a double suspension. At (d) the resolution of the ninth is delayed
until the last crotchet in the bar. At (e) there is a dominant pedal
which is made more interesting by the figure borrowed from bats 3 and
4. This is termed an ornamental pedal. Any interesting rhythmic
figure can be used in this way. It may either repeat the note, or embrace
the notes above and below or the octave below (Ex. 328). There is no
fake relation between the semitone below a harmony note used as
an ornament or as an appoggiatura, as, for instance, the E found in
Ex. 327 (e) and the following bars. There are numerous accented
passing notes in this example. The effect of those at (/), (g), (A), (k)
and (I) should be specially noted.
Ex. 338
THE NINTH
279
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Exercises on the Dominant Major Ninths and their Inversions.
1. Add Alto and Tenor parts.
Add Alto and Tenor. Ninths or their inversions must be used at the asterisks
in this and the following exercises. i InB (, Mi n c Minor I
P
n
* # ' * # # # #6
4
3. Complete the following "by addinj
m
2
arts.
fla
InF Minor
=**
(l). This ninth is never resolved except by the chord progression, (dominant to tonic),
(fc). Major ninth used in minor key. It resolves upwards on to the 3rd of the dominant.
(3). The D in the Tenor is an accented passing-note. The E^ in the Alto is the minor th of
D, the dominant of G.
280 DIATONIC DISCORDS
4. Complete the foil owing. J Q c ^ inor
^
^^
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I
6 7
5 4
|J J J
98 w
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Double Tome Pedal
6. Write a second Gavotte in B minor, making a suitable return to the above
at the end of it. Introduce the chord of the dominant ninth, its inversions,
appoggiaturas, accented passing-notes and a dominant pedal.
THE NINTH
281
7. Add Alto and Tenor. This exercise contains a number of less usual resolu
tions of the ninth. In "bars 1, 5, 9 and 10 it remains to be part of the next
chord. In bar 6 it is the dominant tonic progression and the usual resolu
tion of the seventh in the bass that make the effect of a resolution of the
whole chord, for the ninth itself leaps. The chord in the penultimate bar
is the 3rd inversion of the dominant 9th; C, the 5th,being a suspension.
The bass, F, is the dominant seventh, and does not resolve, but leaps a 4th
to the tonic. The effect is also satisfactory in this case because of the chord-
relationship. The B on the last crotchet in this bar is an anticipatory note.
6 6 4
6
5
6 6
4-
t* 6-
3 4-
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66|46 !e 67694
5
The Ground Bass, that is, a short phrase repeated in the lowest partwith
variations of harmony and counterpoint above it, will form an excellent study
at this point, for it can be harmonized firstly with triads, secondly with
prepared discords, thirdly with accented passing-notes and appoggiaturas,
and finally with unprepared ninths and their inversions. Ex.8*9 includes
some of the more dissonant ninths shown in Ex. 317.
Ex.8S9 I [
r Q i
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282
DIATONIC DISCORDS
ihUjd
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Ground Basses to be treated in a similar way.
8.
9.
10.
r r ir r r ^r~rr
r IJ r II JJ J
Exercises H, IS and 13 are given to practise modulation by enharmonicaHy
changing the chord of the diminished seventh. This chord is approached in
one key and quitted in another. It should appear on a strong beat and have
sufficient length for the change of key to make its due effect.
r^~
E
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it Minor
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THE NINTH
283
i \f L u. ' r -
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= s
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766
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ts -
7 1)6 1)6 |6 b6 6
i. Add Soprano, Alto and Tenor. Supply the harmonies where the Bass is not f ig^
ItoBlfin. [ ' HorjtMinltoCMin, "
6
'6 fe]7
^
oFMin.
6 7 Vt 4 3
5
13. Continue this Prelude for piano by repeating bars 2 and 3 and then enhar-
monically changing the diminished seventh in bar 4 so as to modulate to D#
minor. Modulate normally from that key to B major and from thence to
major. Make this the dominant of A minor and conclude in that key.
^P
284
DIATONIC DISCORDS
The Chord of the Dominant Eleventh.
212. Reference to Ex. 315 will show that the dominant eleventh
resolves by falling one step (/) and (g) ; by rising to the 5th of the
dominant, (h) and (j) ; or by remaining to be a part of the next
chord (A 1 ). This example is in five or six parts in order to show the
complete chords. In four parts either the 5th, 7th or 9th of the dominant
may be omitted, the progression of the parts and the effect of the chord
will settle the question as to which should be left out. It will be seen
from the examples that the 3rd of the chord is always omitted for
the following reasons : it is the leading note and the major 3rd (24) ;
it may be the note upon which the discord will resolve (124) ; and
it lies a minor 9th below the eleventh. The 9th and llth may resolve
together (Ex. 315 (/), (h), (j)), or one at a time (g).
213. Although the llth resolves on the 5th of the dominant when
it rises one step, this note need not be omitted for, unlike the leading
note, it is frequently doubled, and lies at the distance of a minor 7th
from the llth a much milder discord than the minor 9th. Neverthe
less, in four-part work, the 5th is generally omitted (for the same reason
as the root of the ninth is omitted (206)), for if it is present it excludes
a more useful note.
214. The llth, like the 9th, is often merely an appoggiatura.
When both llth and 9th resolve whilst the rest of the chord remains,
as in the first four examples, both notes are appoggiaturas.
215. The first inversion has the 5th of the chord for its bass, the 3rd
of the dominant being omitted. If the 9th and 7th are used the first
inversion is simply a chord of the seventh on the supertonic of the scale,
(Ex. 330 (a) and &)). If the root is present and the 9th omitted the first
inversion is a 4 (Ex. 330 (c)). Likewise the second inversion may be
(Ex. 331 (a) and (c)). The third inversion must have
the ninth as the bass and is always 4 (Ex. 332). The last inversion
with the llth in the bass may be either
either s
3
or
6 5
4 or 4
2 2
the root is omitted in the inversions the original 7th and 9th lose their
or 4 (Ex. 333). When
THE ELEVENTH
285
dissonance and are therefore free notes requiring no resolution. The
resolutions given in Ex. 330 (g), (A) and (j) will be better understood
when the chords of the diatonic sevenths have been explained.
Ex. 330
1st Inversion.
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Ex. 331
2nd Inversion.
(e),
(e)
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5
5
5
5
2
5
3
3rd Inversion.
Ex.333
4th Inversion.
'
(c)
H
3 3
216. The third inversion is sometimes referred to as the chord of
the added 6th, i.e. a triad with a 6th added to it. No doubt it got
this name because, when it is resolved on a tonic chord, it resembles
a plagal cadence (Ex. 334).
Ex.334
(a)
it- n
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ft "
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o
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o
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"
286
DIATONIC DISCORDS
217. The resolutions in minor keys are the same as those for major
keys, except that the major 9th is often used instead of the minor
when the 9th resolves upwards in order to avoid the augmented 2nds
(Ex. 335).
Ex. 335
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218. The chords of the eleventh on the notes of the scale other than
the dominant (Ex. 336) are not often heard, but some of them may
occasionally be used if the 9th and llth are treated as appoggiaturas.
Those of the supertonic and submediant have the same intervals as
the dominant eleventh. That on the mediant is the dominant eleventh
of the relative minor . (Ex. 336 (c)). Those on the tonic and sub-
dominant (Ex. 336 (a) and (d)) are more dissonant, the former having
a major 7th and the latter an augmented llth. The eleventh on the
leading note (Ex. 336 (g)) is the most dissonant, for it has a diminished
5th and a minor 9th.
Ex. 886
W (
i.
219. Exs. 337 and 338 are harmonized to include as many elevenths
as possible in order to show the effect of the chord in a few bars. The
original position is marked : the figures refer to the numbers of the
inversions. The first inversion of the eleventh in a minor key (a seventh
on the super-tonic) has the same notes as the first inversion of the ninth
of the relative major key (a seventh on the leading note). Modulations
are often effected by using an ambiguous chord such as this, which is
approached in one key and quitted in the other. Ex. 338 shows this
at (<0 and (&). Appoggiaturas which might be misleading are marked
" Ap."
Ex.337
Quickly
m
(fiat Cantiones, 1,?82).
m
THE ELEVENTH
287
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Ex.338 (For Piano)
Allegretto
288
DIATONIC DISCORDS
Exercises on the Chord of the Eleventh and its Inversions.
1, Add Alto and Tenor.
W-
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326
54
. Add Alto and Tenor,nsing the chord of the eleventh or one of its inversions
where there are asterisks .
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THE ELEVENTH
289
tih r i
i
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p
1st
Bass
j
,
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2nd Bass (5 parts)
3. Complete the following for piano.Write in four parts throughout.
Alia Marcia
llnC 1 UnG
*=
(a)
Ap.
* *
^
^
290
DIATONIC DISCORDS
_*_
(a) Treat the flattened leading-notes as if they were sharpened.
(b) Write quavers wherever there are crotchets in both melody and bass.
Continue the unbroken quaver-movement until (c)
8. Harmonize the French Carol in Bx. 62. using the eleventh and its inver
sions wherever it is appropriate.
4. Write a simple piano accompaniment to this Irish tune,* Op en the door sofUyf
Use the eleventh at the typically Irish cadences.
Andante tranquillo | (Copyright)
'
Write parts for Soprano, Alto and Tenor above the following Bass:-
r J i r r r ir r r r ir r r r
r ir r r
/Cs
r
THE THIRTEENTH
291
6. Harmonize this Baas, in four parts, then re-write it in broken arpeggios in the
style of the given bars as a study for piano. There are five notes in each
arpeggio figure, bat -the lowest is merely the melody doubled an octave below.
The chord of the Dominant Thirteenth and its inversions.
220. The dominant thirteenth has a more distinct character than
any of the other dominant discords for the resolution by leap given
in Ex. 315 (m) and (n) is peculiar to it, and another example of contraction
by elision (165, 189).
221. If the 7th, 9th and llth are omitted and the root doubled it
has the same notes as the first inversion of a minor triad. Nevertheless
when it is resolved in the same manner as a thirteenth (Exs. 815 (m)
and 343 (a)), it still keeps its character.
222. The thirteenth, especially the major thirteenth, is far more
dissonant when it lies beneath the 7th (Ex. 889). XlXth century
harmony books only allowed it thus when it was prepared. It is more
of a melodic discord than the others, for it is most commonly used^to
harmonize the drop of a, third (either with or without the supertonic)
from mediant to tonic in a melody. It cannot be used beneath the
7th in the ordinary course of part-writing as can the other dominant
discords. If the melody happens to be in a middle part the 18th
sounds quite normal even if it appears beneath the 7th (Ex. 840, (a)
and (&)). It may also be used as an appoggiatura. In addition to falling
one step or a 3rd (Ex. 315 (1) and (m)) it often remains to become the
3rd of the tonic ;triad, (Ex. 315 (?)).
292
Ex. 339
DIATONIC DISCORDS
Ex. 340
I* ,i a) i . i j n . j ^
TO 4 p
h> r
i r 1
^
^
r
223. The 5th of the dominant is generally omitted when the 13th
is present unless it is in the bass, and lies a 9th away from the 13th,
as in the resolutions of the second inversion shown in Ex. 346. If the
5th is omitted there remain the 3rd, 7th, 9th and llth. If the llth
is included the 3rd goes out. This leaves five notes root, 3rd, 7th,
9th and 13th (Ex. 341 (a)), or, root, 7th, 9th, llth and 13th (Ex. 341 (&)).
The root is often doubled when the 9th is not present. Thus there are
four different forms of the original position of the chord in five parts
(Ex* 341) and seven in four parts (Ex. 342) to say nothing of the
inversions.
Ex. 341 (b)
|/j J Uli J 1
U) (d)
. . ,i. J i.
!H
=&=
J
T=-
'^=
f
w
H
j
=
i
Ex. 342
4^
4
pt =
-i
=51=
^-
~ir
' '
r
i j; i
f
224. As it is resolved in three ways, and as the discords 7th, 9th,
llth and 13th may resolve one at a time (Ex. 315 (p)) 9 or two at a time
(llth and 9th in Ex. 315 (o)) in various orders ,and in different rhythms,
it will be seen that this chord offers many possibilities. It is not
necessary or desirable to give examples of all these forms of the chord
and all their resolutions. Some of them are so nearly alike in effect
that it is sometimes difficult to decide which gives the exact shade of
colour desired. Ex. 343 shows seven versions of a cadence with various
forms of the chord, but only one form of resolution of the 13th itself.
THE THIRTEENTH
293
Every student should train his ear to recognise the slight colour changes
not only in these examples, but in others which he should find for
himself.
225. It should be observed :
(1) That the forms of the chord without the 9th or llth are so
much akin to the dominant seventh that the three
resolutions given for that chord in Exs. 292 (b), 293 (b)
and 298 are also satisfactory for the thirteenth. One such
resolution of the thirteenth has already been given (Ex. 343),
the other two will be found in Ex. 344.
(2) That when the 13th is resolved by remaining stationary,
provided the 7th is in the chord, both 13th and 7th will
resolve on the major 3rd of the tonic chord (Ex. 315 (q)).
In four parts, with both leading note and dominant pro
ceeding to the tonic, the result is a very thin tonic chord.
The progression is, of course, harmless when the thirteenth
is resolved on the submediant triad (Ex. 344 (a)).
(3) That the resolution of the 13th by drop of a 3rd is not satis
factory when the llth is present, for the llth is the note
the 13th is about to resolve upon.
(4) That the 5ths which are separated by one note when both 13th
and 9th resolve by descending one step (Ex. 315 (o) and
(p)) are not objectionable, but that actual consecutives
must be avoided.
(5) That, in modern music, the thirteenth is sometimes resolved
by chord-relationship alone (Ex. 345).
Ex. 343
rf^-n
1 j i
1 1
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s r
=
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294
DIATONIC DISCORDS
Ex.345
.-A
1 J 1
pi
*=\
U
<
hi-
L i
= =E
r
i
o
226. The common resolutions of the inversions are given in Ex. 346.
The second inversion follows the same rule as the second inversions
of dominant sevenths and ninths, i.e., the bass must approach and
quit it by step, unless another inversion follows immediately.
Ex. 846 1st Inversion
rf
J J ||
K
l
J
cf
k
^f-
~f_
-f
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^
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4= :
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2nd Invars!
on
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7
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t=1
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THE THIRTEENTH 295
5th Inversion
l J J 1 ,1 1
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1 . -j ,
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+1
\>f r |
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1
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r'r' 1
227. The resolutions of the chord in minor keys are identical with
those given for major keys. The major 9th often appears with the
minor 13th when the former resolves upwards (217).
228. The character of the dominant thirteenth and its inversions
is on the whole weak, and it is beloved of the composers of sentimental
songs (Ex. 347 (a)) and musical comedy (Ex. 347 (6)). The excerpt
from Schumann given in Ex. 348 shows that it can be used without
either sentimentalism or cheap frivolity.
Ex. 347 (a)
Ex. 348
Schumann
(1). -Thirteenth in Bk minor, 7th in the Bass. It resolves on the Bt in the
next bar
(&) The same position of the chord in Dk major, bnt with the minor 9th
written as A^ first, and then (more correctly) as Btk
(3). Thirteenth in At major, 3rd in the Bass. The 5th is present and makes
a strong dissonance.
All the detached semiquavers are chromatic appoggiaturas.
296
DIATONIC DISCORDS
229. When only the root, 3rd and minor 13th are sounding, this
form of the chord has the same notes as an augmented triad. It will
be realised from (210) and Ex. 324 that enharmonic modulation may
be effected by the use of this chord in a similar way to that of the
diminished seventh. Ex. 349 show r s each of the three notes treated
as a 13th.
Ex. 349
C minor B minor
i
-u
TT
TT
13
minor
?
f
T=*f
230. In Ex. 350, thirteenths are marked (1); accented passing notes
(2) ; retardations or upward-resolving suspensions (3). The latter are
appropriate for notes such as leading notes with a strong tendency to
rise. It naturally follows that if such notes can be used as appoggiaturas
they can also be prepared.
Ex. 350
Andante
Violin
I
(1)
CD
m
m
(8)
THE THIRTEENTH
297
I
CD
m
r ,f f
a;
(2)
JT~Y-
r if i i ir'
(1)
(1)
fll
J. M
298
DIATONIC DISCORDS
231. In Ex. 351 the various forms of the chord of the thirteenth
are marked (1), At (2) the At] resolves both the llth (Bj?) and the
9th (G). At (3) there is an example of a chord approached in one key
and quitted in another. In the key of A|? from which it is approached
this chord is the 1st inversion of a dominant ninth the A[? in the
L.H. may be regarded as an appoggiatura. It is quitted as a dominant
eleventh with the 9th in the key of F minor. The chord at (4) is
approached as the 1st inversion of the tonic triad in G minor, and
quitted as the dominant thirteenth in E|?. Nos. (5), (6) and (7) are
examples of the enharmonic change of the minor thirteenth explained
in (229). Ex. 351 is really too short for so many abrupt modulations ;
the same may be said of Exercise 6 ; there is not time in a few bars to
create a sufficiently exciting atmosphere. But these examples are
included so that the student may gain a knowledge of the effect of the
thirteenth used in this way.
Ex. 351
Scherzo
THE THIRTEENTH
299
300
DIATONIC DISCORDS
Exercises on the Chord of the Thirteenth .
1. AM Alto and Tenor. Write chords of the thirteenth or their inversions at
the points marked with asterisks in this and the next two exercises.
fl 'in G III
i % $ =M^X r r r j ^
a?
ii
n
4v t; * zf ft f* E--P ^ t=z:
i
_
r
^
i 1
-' * V ! UJ *- ' P"^^^
* * * "
JJ J
*
Mj- ^^i
9 113 *
* (Tonic Pedal)
^ ^ 'In A minor In E minor
-Jt. -h J __k J ^ p E m f^ |
L .
, ,
8> r J ' * J - p r ^
tji J J ^= -4 fr-U K
=1=
=
-
F
j ^
A J*^ ^ g^^-^s^^^-
(with major 9th)
*
=
thq
+
r
(In 5 paxts)
I J J K , L . | ^ | | | i g
1
1 1 *-
$ J n^-j-J^ ^ H ! J- ^J^
"> J ' J ^ 4^- ^TT]
-*- 1
^
4
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-r^ -^r^
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*-* *
* * *
*
THE THIRTEENTH
301
r J^J p
llnf
^
r p
P^
. Add Alto and Tenor to the first four, and Soprano and Tenor to _ the last
four bars.
1 In E minor
"* rn*~
F=h
1 J7j | i |
fo I
fcytt*- t = f f
r LJI
F 1
> * ^ m h-
III.
> f *\ * r r r -
Vr * *
2 1^ ff r | j 4 4 *
^ ^
llnC llnA^inorl
^
3. Add Alto, Tenor and Bass.
i
^
llnCl In F , I In B!>
NJJ i IJJJJ l
*
4. Add three parts using thirteenths where they are appropriate. Write
for piano.
802
DIATONIC DISCORDS
5. Add three upper parts, supplying the harmony where the Bass is not
figured.
1 jo R I > JIQ*
13 5
7 8
13
7
V
7
3
13 6
9 H
"8
6
5
7 is
7
6. Add the three upper parts. At (1) use the 4th inversion of the thirteenth,
(7th in the bass) with the 9th and major 3rd from the root. At (2) use the
1st inversion of the dominant 9th in ik At (8) use the dominant eleventh
in minor, (7th in the bass, 3rd inversion) with, the 9th and 5th from the
root .At (4) use the chord of the aug. 5th in C minor, but resolve it in B minor.
At (5) use a thirteenth in C major in its original position. At (6) use the
same chord in A minor.
*> 1 J J
I
=H=F
i j j i
r i t-H
1 T 1
7' / 4 B * J
(1)
I *pr
4 4 ?
5 -M
'4 TtJ '
"P [-73 FT
(8) (1
k)
IT J
(5)
-f JT
(6)
1 -* B
SECTION XVI.
THE DISSONANT TRIADS AND DIATONIC SEVENTHS.
232, It has been shown that dissonant triads and diatonic sevenths,
other than the dominant seventh, are sometimes parts of other discords.
They are also often employed in such a way that they can claim no
relationship with any other chord, and have a separate existence of
their own. This aspect of them has been postponed until now, since
their common use as parts of other chords made it necessary to explain
first the chords from which they are derived.
Dissonant Triads.
233. The first inversions of the dimiiiished triads have already
become familiar in the contrapuntal sections of this book. The original
position is a thin-sounding, rather useless chord. Occasionally the
part-progression may be improved by using it instead of a first inversion
of a dominant seventh, as in Ex. 318, or instead of the second inversion
of a minor ninth without root, as in Ex. 352, for it is obvious that to
include a G in Ex. 318, or a G# in Ex. 352 would break the onward
march of the 3rds in contrary motion. Its use in a sequence has also
been shown in Exs. 316 and 317. Obviously the bass note and 5th
are bad notes to double when it is an incomplete dominant seventh,
for they are in reality leading note and 7th. When it is part of the
minor ninth the bass note is the best note to double, for it is the 5th
from the dominant, the actual root ; the other two notes, the 3rd and
5th, being respectively the dominant 7th and 9th. When it is an
independent chord the bass can be doubled even though it is the leading
note.
Ex. 353
234. The second inversion is found even less frequently than the
original position of the chord. It is sometimes of use in a sequence
such as that given in Ex. 353 (a), where similar harmonies are found to
those in Ex. 316 (b), but where the bass remains, instead of descending
a 5th to the resolutions of the sevenths. Even here the effect would
be richer if an inversion of a seventh were made to take the place of
each *, as in Ex. 353 (b). The 4th and 6th may also be treafed as two
appoggiaturas, as in the cadential * (Ex. 354).
303
304
Ex. 353 (a)
DIATONIC DISCORDS
Ex. 354
"
Ex. 353 ft)!
235. The augmented triad is of a different kidney, and is a strong
and healthy fellow when used aright. Its use as part of the minor
thirteenth has been already discussed. It often appears, however,
in such a way as to present no likeness to that chord. In common
with most other discords it can resolve on the chord whose root lies
a 4th above or a 5th below its own (Ex. 355). This brings us to an
important feature of harmony which has not hitherto been investigated.
It is this : a progression of chords which gives a satisfactory effect
in one key will also do so in any other provided that it is preceded and
followed by harmonies related to both keys. Thus the resolution
of the augmented triad given in Ex. 355 in C minor sounds just as well
in the keys of Eb and A|? (Ex. 356 (a), (b) and (c) ). The use of this
chord in the two latter keys involves a note foreign to the scale, but
one which does not change the key. The technical term for all such
notes is " Chromatic." The plan of this book is to put the horizontal
before the vertical to make sure that the student can draw freely
before a palate of many colours is given to him. Chromatic harmony,
therefore, will be discussed last. However, there is no need to split
hairs, and if the progression in Ex. 355 can be used, there is no reason
why that in Ex. 356 should not be used also, even though it is
chromatic. It will serve as an introduction to what will follow at a
later stage.
Ex. 355
7T1
: >j -b r: ~i
a;
1 IT** 1
H
U
u
*=
^
i :
u
-e-
(S
1 ' P K H
Ex. 356
DIATONIC SEVENTHS
(b)
305
The inflection of any one of the notes of an augmented triad a
semitone upwards produces a minor triad, or one of its inversions
(Ex 357 (a)) and a similar inflection downwards produces a major
triad or an inversion of it, (Ex. 357 (b)). If two notes are inflected
upwards simultaneously the result is some position of a major triad,
(Ex 357 (e)) Likewise if two notes are inflected downwards, the result
is some form of a minor triad, (Ex. 357 (d)). Any one of these semi-
tonal movements is quite sufficient to resolve the augmented triad,
'in settling which note to double avoid the inflected note and the
sharpest note in the chord. A keen ear will detect the latter without
help Those with less acute ears can calculate it as follows. The
sharpest note is always the tonic of the key with the greatest number
of sharps or the fewest number of flats. Thus E is the sharpest note
in the chord of C, because E has four sharps, G one, and C none in their
respective signatures. B flat is the sharpest note in the chord of G flat,
because the key of B flat has only two flats in the signature, whilst
D flat has five and G flat six.
Ex. 357
W
im
236 Diatonic Sevenths. These have four common resolutions :
(1) On to the chord whose root lies a 4th above or a 5th below.
(2) On to the chord the root of which is on the degree of the scale
next above the root of the seventh.
(3) The 7th itself may remain to be part of the next chord.
(4) The 7th may be treated as an appoggiatura.
It is quite natural that these chords should sometimes resolve in
the same way as dominant sevenths (Exs. 292 (b), 293 (b), 298), for
306
DIATONIC DISCORDS
they are akin to them in sound. If a comparison is made between
Exs. 358 (a) and (b) it will be observed that (a) has 1 a bolder and slightly
more dissonant effect than (6), and also that the; 1 leading notes in (6)
are obliged "to rise, but in (a) have a free movement. Composers of
the mid-nineteenth century were more inclined towards the softer and
smoother seventh in (6), indeed they sharpened the major 3rd as often
as they could, and flattened or diminished the 7th. For this and
other similar reasons their music often- lacked boldness and strength.
Ex.358
a*
r4
-1 r-
1 1
_j ^ |
i ,
n
*
4
-f
i=f
1 *
> :
i
J
FT
^
i
r
237. To take the diatonic sevenths seriatim, the Tonic Seventh
(Ex. 359) has all four resolutions in the major, but only one (No. 4) in
the minor if the leading note is sharp (Ex. 360 (&)). If it is flat,
however, as in the descending melodic minor, all four are applicable
(Ex. 360 (a) and (c)).
Ex.859 (a)
i
8.
4.
xc
me
m
Ex.360 (t
]\ i
%
j
v
i
t
. K
f
f
>.
1 f
r
r~4
h=
|
.- ^
i
=1
-t C
Jte=* :
8.
Ex.360ft) Ex.860 fr)
. * ,
o
U:
DIATONIC SEVENTHS
307
'238. The Supertonic Seventh often resolves on a second inversion
of the tonic triad (Ex. 361), but if the 6th of this chord is regarded as
an appoggiatura then the 5th of the following dominant triad is the real
note of resolution, the 6th being only an ornament. The resolution
then corresponds with that of an inversion of the eleventh, (Ex. 330 (j)).
All four resolutions can be used in both major and minor keys. In
the minor the 5th can be sharpened when it rises.
Ex.861
239. The Seventh on the Mediant has four resolutions in major
keys. In the minor it can only resolve on the submediant if the
leading note is sharpened, but when the leading note is flattened and
descends the other three resolutions can be used (Ex. 362).
EX. sea
240. The Subdominant Seventh resolves on the diminished triad
on the leading note when the bass rises a 4th or descends a 5th. This
progression is most frequently but not always found in sequences,
(Ex. 363). Resolutions 2, 3, and 4 are all available. In minor keys
the 3rd may be flat or sharp according to whether it falls or rises.
EX. aea Ex.364
%=t
J
>
L
A
t r
-f-*
f
u
r
* \
h=|
L 4
U f 1
4
1 f
241. The Submediant Seventh when given resolution 2 resolves
on the diminished triad, (Ex. 364). Like the subdominant seventh,
when given resolution 1, it is often found in sequences.
808
DIATONIC DISCORDS
242. The Seventh on the Leading -note has all four resolutions
in major keys. It is a diminished seventh in minor keys, and if given
resolution 1 the bass (the leading note) would either di*op an augmented
5th an awkward progression or a rise a diminished 4th. The latter
can be used occasionally, but the diminished 4th must be resolved by
allowing the bass to proceed either to the tonic pr the supertonic,
(Ex. 365). The seventh on the flattened leading note in minor keys
is often useful. If givdn resolution 1 it corresponds to the dominant
seventh of the relative major. But it can often be used without
giving the impression of a modulation to that key if the original tonality
is strongly established before and after this progression (Ex. 366).
Ex. 865
Ex. 866
n
"""
243 Exs. 367 and 368 are attempts to show what strange
and sudden modulations can easily be effected by the inflection of the
notes of the augmented triad. As was stated in (231), short harmony
exercises are not appropriate for such key changes. The musical
object of them is to mystify the listener as to the tonality. That is
why they occur in the middle of a composition, for then the original
key can be firmly established before and after. Vagueness for its own
sake is a vice and not a virtue. It is only useful when used as a contrast
to clear definition. If modulation may be compared to a journey (87)
then vagueness of tonality suggests that the traveller has lost his way.
The excitement this engenders is not so pleasurable in itself as the
moment when, by some stroke of good luck (or ingenuity) he finds his
way home again.
Ex. 867
I 4
iiJ
DIATONIC SEVENTHS
309
l-
Ex. 368
244. Ex. 369 contains the double appoggiatura. This is formed by
proceeding from the upper appoggiatura to the lower and then to the
harmony note, or vice versa, (104, Ex. 100). It may be written in
two ways, so that either the first appoggiatura or the second gets the
stronger accent. In Ex. 369 the first kind are marked by a -slur, and
the second by a square bracket. It will be seen that appoggiaturas
can be used with a discord as well as with the notes of a triad. The
student must be the judge as to whether they create too much dis
sonance. In Ex. 369 the sevenths are marked. Roman figures refer
to the degree of the scale upon which the seventh is built, ordinary
figures to the four different resolutions given in (236).
DIATONIC DISCORDS
Ll.
ILL
vn.s. vn.s.
$
j a
-LJ:
w
Jr-
vn.4. vi.4.
vn.4. vn.. iv.4. iv.4. n.i.
Exercises an the Dissonant Triads and Diatonic Sevenths.
1. Add Alto and Tenor.
7 76 6 83 e 76 43765
DIATONIC SEVENTHS
311
2. Complete the following in three parts for piano. Diminished triads oconr
at (a), augmented triads at (b).
Tempo di Gavotta
S. Add Soprano, Alto and Tenor.
To B minor
(*)
/6
U
ft) ft)
To F major
(ft)
("i)
ft)
(I)
(2 I!)
4. Beginning as indicated, complete this as a short study for piano, first
writing a skeleton, as on the first two bars of the upper stave below.
DIATONIC DISCORDS
cresc.
dim.
Conclude the study with original -work.
5 Add Alto and Tenor. Diatonic sevenths, or their inversions, occur at the
asterisks. ^- ^^ Ap.
i
Ap.
Ap.
m
* *
p y
(65)
DIATONIC SEVENTHS
313
(l?6)
* *
* *
* *
^
m
314 DIATONIC DISCORDS
SECTION XVII.
FREE COUNTERPOINT.
Answering Fugue Subjects and the writing of Counter-Subjects.
245. The student is now equipped harmonically for 'writing free
counterpoint. This type is more easily learnt from the works of
J. S. Bach than from a book. All composers from Bach's time onwards
who have written counterpoint easily and effectively have profited by
their knowledge of these masterpieces, even though their own per
sonality shows itself, as it should do, in the music they have written.
Acquaintance with Bach's clavier and organ works alone is not
sufficient. The cantatas, oratorios and other instrumental works should
be included.
246. As in the earlier and stricter style it should be the counterpoint
which dictates the harmony, not the harmony which dictates the
counterpoint. For instance, in the exercises on writing imitations on
a hymn-tune or chorale, the tune itself will bring into the mind auto
matically certain harmonic progressions. But these must often be
discarded or modified to allow the parts to move in the conceived plan.
247. Those who have worked through the former sections of this
book should not find in free counterpoint anything but the natural
enlargement of the principles embodied in that of the XVIth century.
The main differences are as follows :
(1) Leaps of diminished 4ths, diminished 5ths, major 6ths and
major or minor 7ths can be used, the general principle of
returning in the opposite direction being still observed.
Though this need not always be by step, the return should
usually be to some note within the interval by which the
leap was made.*
(2) The chord of the thirteenth, except when used as a plain chord
of the sixth, is not very suitable, as it stands to reason that
chords with a fixed progession in every or nearly every part
will only hamper music in which the free movement of each
part is so essential to its vigour and vitality.
The most useful harmony will comprise :
(1) All the XVIth century harmony.
(2) Retardations and suspensions of discords.
* Sometimes the general contour of the phrase warrants a departure from this guiding
principle, as in Ex. 389 (/), where the figure is palpably founded on a dominant
seventh on F, and is also a diminution of the forthcoming phrase of the C.F.
FREE COUNTERPOINT
315
(3) Accented passing notes, often clashing, provided that the parts
moving by means of them are carrying on to some pre-
ceived point a,nd not moving for the sake of movement.
(4) Appoggiaturas, both single and double.
(5) Prepared and unprepared discords and their inversions, the
chord of the seventh coming first in frequency and first in
usefulness.
(6) Discords the resolution of which is either deferred or transferred
to another part.
(7) Pedals, double and single, ordinary and inverted.
248. When inventing contrapuntal themes it will be found that
those of small compass and fairly conjunct motion are the easiest to
work, and those with incisive, arresting rhythms the most effective.
249. The first exercises in free counterpoint should be the writing
of counter-subjects. No one can claim to be a contrapuntist who,
having been given, or having invented one tune, has not sufficient
imagination to write another to fit with it and act as a foil to it.
250 Counter-subjects are most useful in composition when they
are in double, or invertible counterpoint, that is, when either subject
or counter-subject can be used as a bass. Movement by step always
gives a sound bass ; incongruity being caused by the use of certain
leaps It is the inversion of intervals consequent upon the inversion
of the two parts that creates whatever difficulty there may be. The
intervals of the 3rd and 6th give no trouble (13) ; it is the 4th and 5th,
and to a less extent the Tth and 9th that need to be watched. If the
upper part leaps from the interval of a 5th in the original version, the
bass wffl leap from the interval of a 4th in the inversion. This may
involve the quitting of a $ or 5 contrary to the rules laid down in (184)
and (196) (Ex. 370). The interval of the 9th becomes a Tth when in
verted If it is resolved as a 9th in the original version a good deal
more dissonance will appear in the inversion (Ex. 371). When resolved
as a 2nd there is no difficulty (Ex. 372).
Ex. 870 (a)
316
DIATONIC DISCORDS
251 Intervals greater than an 8th in the original cause a crossing
of the' parts when inverted, (Ex. 373 <*))-., Tb* >V "e m-
01 me paiw. ins can a i way s be avoided by transposing the
S^alSi^rf-nrth&wer (Ex. 373 (c)). But this is
oLasioSv awkward or impossible in the course of a fugue or contra-
STcomposition because of the consequent gaps between parts,
^extended compass. Double counterpoint " at the octave" is
consequently more useful, generally speaking, than double counterpoint
" at the fifteenth."
Ex. 378
r
^
252 Double counterpoint can also be written at the 10th
(Ex 373 (d)) and 12th (Ex. 373 (e)), in which cases the upper part is
transposed down either a 10th or a 12th. When writing in this way
it S increasingly necessary to bear in mind what each interval will
become wTen inverted. The simple formula (a-b) + 1 wiU show this,
a = The interval at which the double counterpoint is to be written
either an 8th, 10th, 12th or 15th.
b = Any interval between subject and counter-subject.
Thus, if the double counterpoint is at the 12th, and the interval between
Sect and counter-subject is, for instance, a 4th, then that interval
when inverted will become a 9th, for (12-4) + 1 = 9.
253 Although this book does not treat of Fugue, which is a separate
studv it should be a preparation for that form of composition. There-
ffit here seems needful to explain the traditions of fugal answers.
For in a fugue, after the subject has been announced, the second voice
or instrument, or part to enter does so with the " Answer," whilst the
first part continues with the counter-subject.
254 If the subject is entirely in the tome key, and if the fifth note
of the scale does not occupy an important position at its commencement,
the answer is simply the subject repeated in the dominant key. It
I then 7a?d to be a " Real Answer.'' But if the subject modulates to
the dominant, or if at its commencement the fifth note of the scale is
prominent, then certain modifications are made in the answer and it
is then termed a " Tonal Answer."
FREE COUNTERPOINT
317
These modifications are therefore of a twofold character : (a) those
made to prevent modulation to the comparatively "distant key of the
supertonic; (b) those which originated, in the two'forms of the modes,
authentic and plagal (142, Ex. 220). Let us consider them separately. *
255. (a) Changes to prevent too extraneous a modulation.
If the subject modulates to the dominant and the answer is an exact
transposition of it, then the answer will modulate to the key of the
supertonic (Ex. 374 (b)). But as the next part to enter with the
subject will be in the tonic (in Ex. 374 it wilj.be in E[?) a modulation to
such a distant key (in Ex. 374 the key of F) would be most awkward.
Therefore the following rule is observed : * , ^
That which is in the tonic key in the subject is transposed a 4th
lower or a 5th higher to the dominant key in the answer, and that
"which is in the dominant in the subject is transposed a 5th lower or a
4th higher to the tonic in the answer (Ex. 374 (c)).
In some subjects the rhythmic figures or phrases are clearly divided,
as in Ex. 374. It is then easy to find where the change should be made.
In others the figures may be linked together, or the subject may consist
of only one figure. In these cases there are two points to remember.
The first is that modulations in fugal answers are no different from
other modulations : that is, they should take place as early in the phrase
as possible. Get to your destination by the quickest route without
wasting time (84, 87),
The other point is that no violence must be done to the melodic
outline of the subject. These two points must be taken in conjunction,
but the second is naturally more important than the first.
Things to be avoided are :
Jerky and unnatural modulations.
Tautophony.
Awkward intervals.
The breaking of sequential figures, or of the melodic shape of
the subject.
Ex. 874
J.S.Back (48. Book 4. NO 7)
It goes without saying that every note in the answer must bear the
same relationship to its tonic as the corresponding note in the subject
bears to its tonic. Ex. 375 (a) might be regarded as being in C, G or
E minor, or it might be argued that the first four notes were in C and
318
DIATONIC DISCORDS
the rest in G. In the first three cases the answer would be as at 375 (h]
or, if it were in C, alternatively as at 375 (c). If only the first four notes
were in C, then the answer would be as at (d) or (e). But in no case
could they be as at (/), for the third quaver of the subject, B must
be either the leading note of C, the mediant of G, or the dominant of
E minor, and the corresponding note in the answer must bear the
same relationship to the three dominants of those keys, namely, G D
and B -minor. But in each case this note is F#, not Ft|. This' point
has been dealt with at some length because so many mistakes arise
through overlooking it. If the transposition is carefully done no
mistakes can occur. *
Ex.375
If either a real or tonal answer is possible, the tonal answer is
generally more satisfactory because it presents variety, and in some
curious way does seem to give an " answer " to the question asked by
the subject. Ex. 376 (a) (Bach's Wohltemperierte Klavier, No. 23,
Bk. 1*) would normally be regarded as being entirely in B, and would
have a real answer as at (b). Bach took the unusual view that the
notes under the square bracket were in F# and thus arrived at the
tonal answer (c).
Ex. 376
* Hence forward referred to as the <f 48."
FREE COUNTERPOINT
319
Occasionally, to avoid ugliness, it is necessary to regard the tonic
as the subdominant of the dominant. Ex. 377' would at first sight
seem to be in F up to the first quayer in the third bar, in which case
the ugly and tautophonous answer at (b) would result. But if the
portion in square brackets is regarded as being in the subdominant of
C, then, in the answer, it will be in the subdominant of F, which gives
a much more satisfactory result. The modulation is then made
between the two rhythmic figures, not in the middle of the second one
the symmetry of which is thus unspoilt.
Ex. 377
* <W , r i
r~"P
'
J
I*
.
-$ * ^ IJ. O* J
1
i
<3 * -J- ^s ^* ^
*H
i^a
J-31
==
Similarly in the fugue in G$ minor (48, Bk. I, No. 18) Bach preferred
to regard the wh,ole subject except the fii$t note as being in D$ minor,
the second note to the seventh in the subdominant of that key, rather
than alter the shape of bar 2. Thus, in the answer, this section is in
C# minor, the subdominant of the tonic answering the subdominant
of the dominant. Technically, in this and similar cases, the answer
is the subject. That is, if the answer is answered in the normal way
the result is the subject. But emotionally the opposite is true.
Ex. 378 (a) is a parallel case. The normal answer appears at (fe), but
has a jerky modulation the C# and A|; do not agree together. The
best answer is (c) which is arrived at by arguing that the whole of the
subject is in G minor except the first note.
Ex. 378
Ex. 379 (a) is a subject (by Dr. George Dyson) which makes even
more use of the subdominant. It begins in the subdominant of F and
from the second bar is in the subdominant of C, actually arriving in C
at the last bar ; (b) is the normal answer and (c) the better one.
320
DIATONIC DISCORDS
Ex. 379
(a)
256. (b) Note -alterations originating in the authentic and plagal
modes. The classical rule is as follows :
When the dominant or dominant and tonic (notes not keys) occur
as prominent sounds at the beginning of a subject, they are reversed
in the answer dominant answers tonic, tonic answers dominant.
Key transposition ensures that dominant will answer tonic, but not
that tonic will answer dominant. Examples have already been given.*
These note changes are not arbitrary. In some cases they give variety
and character to the answer ; in others they spoil the contour. The
latter is often the case when the notes of the tonic triad succeed each
other. Ex. 380 (a) would never be answered as at (b). Bach in his
short organ fugue in G minor makes no note-alteration for this reason
(Ex. 381). But there are cases in which the notes of the tonic triad
are heard in succession where a tonal 'answer is best. This is usually
when the dominant occurs on an accent and at a change of harmony
as in Ex. 382 (48, Bk. II, No. 3).
Ex. 380
(a)
(b)
Ex. 881
0)
Ex. 382
s. 374 (^) and 375 (c), (e)
FREE COUNTERPOINT 321
257. Counter-subjects, The counter-subject begins before the
answer or after it, but not with it. The second part to enter usually
does so a 4th, not an llth below, or a 5th, not a 12th above the subject.
The counter- subject must have sufficient character and contrast
with the subject to be recognised at each subsequent entry. It cannot
be called a " subject " if it is a mere string of notes that happen to
fit with the theme. The counter-subjects of the following fugues from
the " 48 " should be carefully examined :
258. Book I.
No. 2. Contrasted rhythm. Inversion at bars 7 and 15.
No. 3. Two counter-subjects in contrasted rhythm.
No. 4. Two counter-subjects, the first entering at bar 35,
the second at bar 49.
No. 6. Counter-subject combined with inversion of subject
at bar 27.
No. 7. No. 10, (Irregular answer.) No. 11.
No. 12. Three counter-subjects as shown in Ex. 383.
Nos. I and III are examples of a telling type of
counter-subject having short, incisive rhythmic
figures separated by rests and repeated sequentially.
No. 13. Note the repetition of the figure.
No. 14. Another example of a repeated figure, but one of a
different type to No. 12. Really Ex. 384 split up.
No. 15, No. 16. Very like the subject in rhythm, but with
the figure inverted.
No. 18, No. 21. Two counter-subjects, the second of the
type seen in No. 12.
No. 23, No. 24. Note the answer.
Book II.
No. 1. (Sequential figure.)
No. 4. Bar 20 upper part.
Nos. 6, 8, 9, 10, 13,
No. 14. See bars 20 (C.S J ), 28 (C.S.I, and Sub,).
34 (C.S.I, and Sub.), 36 (C.S.2), 56 (Sub. varied,
C.S.I, and C.S.2), 61 (the same inverted), 68 (the
same again inverted).
Nos. 15, 16.
No. 17. (Plain C,S. in harmony notes.)
No. 18. See bars 61 (C.S.I) and 97 (Sub. and C.S.).
Nos. 20, 22, 23, 24. See bar 35 (C.S.2).
Many of these subjects and counter-subjects are variations. The
skeleton theme, upon which the harmonic progression is based, is
clothed by the composer's imagination with all kinds of figures. For
instance, the subject of No. 14 in Book II is a variation of Ex. 385,
and the subject of No. 19, Book II, is a variation of Ex. 386. Before
attempting to write counter-subjects to the given themes students
should take similar sets of notes and vary them in as many ways as
322
DIATONIC DISCORDS
their imagination can invent. One set of such variations is shown in
Ex. 387.
The means of variation are as follows :
(1) Repeated notes.
(2) Passing notes.
(3) Changing notes.
(4) Appoggiaturas.
(5) Sjnicopations and suspensions.
(6) Leaps to harmony notes.
Some few subjects consist entirely of harmony notes without variation
(48, Book I, Nos. 4, 12, Book II, Nos. 9, 14 (except for the repeated
notes), 23). But most of them are either entirely varied or a mixture
of the two. Counter-subjects are the same, though a counter-subject
entirely in harmony notes is seldom met with. Contrast is obtained
by making the counter-subject more ornamental where the subject is
plain and vice versa.
Ex. 383
Theme
s
Ex. 884
JM|' yf r
r "i in
FREE COUNTERPOINT
323-
Ex.385
Ex. 386
rr.f f r
Exercises on writing Counter -Subjects.
i. Vary the themes given below on the lines of Ex.387 and the Bach exam
ples quoted. ( \
(a) (b) ii ,
rrrfr n
(el
824
DIATONIC DISCORDS
I. Write answers and counter-subjects to the fallowing fugue subjects:
t \
Allegro moderato
(A)
Allegro moderate
Allegro moderate
i
Viola
(e \ ^nd Violin
1 y Allegretto
(/) 1st Violin
Scherzando
FREE COUNTERPOINT
325
ft) *
There was a young la - dy of Ni - ger, Who
went for a ride on a ti
Words for the Counter-Subject :
They came back from that ride
With the lady inside,
And a smile on the face of the tiger.
ft)
Allegro non troppo
Larg-o,risoluto
m
If aU "be true as I do think.There are three reasons we should drink;
Counter-Subject (mostly in quavers) :
Good wine a friend or being dry
Or lest we should be by and by
Or any other reason why.
Henry Aldrich
Scherzando
p p
3E
dev-il hav-ing nothing else to do Went off to
w*
ml
^=
J P P P =
^^
T t
^
X _ .
*=
Counter-Subject :
My lady, tempted by a private whim,
To his extreme annoyance, tempted him.
H. Bdloc.
* Some of the above subjects have been set to words because the words sometimes
suggest rhythmic figures which the music alone would not.
82G
(n)
DIATONIC DISCORDS
Serioso
p ir r r p ir
_ . . _ , '
r
Trea-son willnev-er pro s-per ; - What's the re a- son, what's the
Counter-Subject :
For if it prosper, none dare call it treason.
John Harington.
Imitations on Ground -basses and Hymn-tunes or Chorales.
259. Free counterpoint may now be written using ground-basses
and hymn-tunes as C.F's. These give a ready-made framework on which
to exercise ideas, like the traced designs of fancy work. They are also
a good preparation for the composition of fugues. Ex. 388 shows the
style for ground-basses. It will be noticed that the last repetition of
the bass is varied and imitated in its varied form.
Ex. 388. Double appoggiaturas are marked by square brackets.
i
r r t
1E^
trr
r
FREE COUNTERPOINT
327
260. Counterpoint and imitations on a chorale or hymn-tune may
be attempted in the three forms shown in Exs. 389, 390 and 391. The
intervals of the themes used for imitation can be altered to fit different
situations, but this must be done in a reasonable manner. A 4th is
so like a 5th that these two intervals can always be interchanged (256).
Any other interval can be made larger or smaller by one degree (Exs. 389
and 390 (a)), but beyond this (Exs. 389 and 390 (&)) there is always
the danger of making the themes unrecognizable. The same applies
to alterations in rhythm (Ex. 389 (c)). Slight alterations, such as
the substitution of a dotted note and short note for two of equal length,
or the doubling or halving of the length of two equal notes will not
take the character from the themes. But their accentuation must
not be interfered with, for, unlike XVIth century themes, they depend
so much on the bar-accent and on time-divisions that if these are much
altered their identity is lost. The themes need not always appear in
their entirety (Exs. 389, 390 (d))> Here again common sense must
be exercised ; enough must be heard to make musical sense. The
free parts those which for the time being are not concerned with the
theme can often be developed from it (Ex. 389 (e)). The forms
of the three examples given are taken from Bach (although, of course,
he used many more forms) and will be found most useful at this period.
They are as follows :
261. Ex. 389. This begins with an introduction, or prelude,
wherein all the parts, except that which sings the C.F., enter successively
with a diminution* of the first phrase of the C.F. When the C.F.
enters the diminutions are combined with it. This plan is followed
throughout. Interludes of a few bars are formed by writing imitations
on short themes which are diminutions of each successive phrase of the
C.F. These themes are afterwards combined with the C.F. A few
* The diminution of a theme is the theme written in notes proportion ah ly shorter
than the original length. Augmentation is the opposite the theme written in ttotts
proportionately longer than the original.
328
DIATONIC DISCORDS
bars may be added as a coda. The device of inversion may also be
used, i.e., the theme with all its intervals inverted, or approximately
inverted (Ex. 390, at (g)). Examples from Bach : Cantatas. No. 2.
(*B and H) Ach Gott, vom HimmeL No. 4 (N) Verse 4, Christ lag in
Todesbanden. No. 28 (N) chorus, Now praise my soul No. 38 (N)
Aus tiefer Noth, first chorus. No. 121 (O.U.P.) Christum wir sotten
loben, first chorus. No'. 182 (O.U.P.) Himmelsk'onig, sei willkommen
seventh movement. No. 112 (N) chorus, The Lord my faithful
Shepherd is.
Ex. 389
Maestoso
fc. Jfa ry
ijQ i
B=2
i - 5= ;
I f
f . , c) i, J j' i
y
-.- ]
i rH
* [
<?)
1 r. r r r **
J f ] J | J =E
fa)
P = ^-
1
rf r d ^ ^
1
r i r r f P
M=J
J --L .
*B.
6- H. - Breitkopf & Hartel
. JV. -
Novetto. O.U.P. - OA/ard University
FREE COUNTERPOINT
829
cresc.
^
Jj J r. j
.fo
cresc.foco afoco
r r r r
s
|g
cresc.focq afoco
?C./(
330
DIATONIC DISCORDS
262. Ex. 390. This has the same form as the preceding except that
here the themes are not diminutions of the C.F. and therefore do not
alter with each phrase. One or two themes are invented and these
are combined with the whole of the C.F.
Examples from- Bach: Cantatas. No, 3 (B and H) Ach Gott, wie
manches Herze leid, first chorus. No. 1 (N) (Forms 1 and 2 combined),
Wie schon leuchtet der Morgenstern, first chorus. No. 26 (O.U.P.) Ach[
wiefluchtig, first chorus (combination of forms 1 and 2).
Ex. 390
Moderate
Old
(Theme II)
mf
^
H=i
rnf
(Theme l)
W
FREE COUNTERPOINT
331
I^J J J
m
3=3=*
332
DIATONIC DISCORDS
m
cresc,
m
j f err r
* /*^
i
cresc*
fe-
1
Wft)
FREE COUNTERPOINT
383
263. Ex. 391. It will at first be found easier to write the two
previous types entirely for voices, but the form in Ex. 391 is essentially
instrumental. Bach wrote for a full choir in addition to the accompani
ment which consisted of a figured bass for organ or harpischord and a
varying number of other instruments. All this may be attempted later*
The all-important jtoint at the moment is for the student to practise
writing what is practically a descant to the C.F., and to write it in such
a way that it forms a beautiful melody independent: of the tune. This
melody is given unity by weaving into it some fitting rhythmic figure
and developing it throughout. The melody should be in the upper
most part and the first sentence of it should appear initially without
a hint of the C.F. in order to give the pleasant surprise of hearing the
melody combined with the C.F. at its repetition.
Examples from Bach : Cantatas. No. 147 (O.U.P.) Jesu, Joy of
man's desiring, chorus. No. 140 (B) Sleepers wake, tenor chorus.
No. 22 (O.U.P.) Awake us, Lord, chorus. No. 6 (N) Bleib bei uns,
soprano solo, third movement. No. 31 (O.U.P.) Der Himmel lackt,
soprano solo, sixth movement.
264. The choral prelude offers a very good opportunity for the
commencement of five-part work, for, as the part to which the
the C.F. is assigned enters intermittently, five parts will only be required
here and there. Unisons proceeding to octaves or vice versa and doubled
major thirds may now be more frequently employed. Discords must
not be doubled. The distribution of the movement between the five
parts will probably mean that each one moves less than in four-part
work, and that longer notes will therefore occur oftener in all parts.
334
DIATONIC DISCORDS
Ex. 391
F - Andante tranquillo
'Herr Gott Vater*
;^ = ^
3
V
i..i n . =F=
^ \
1
*e
H
*==
1 ,
|
, i **
I
L f
J J J .
f-r-T
-
I
^ JJ r J -
3=F=
u-
FREE COUNTERPOINT
335
cresc*
A
^^
p
^E
cresc.
886
DIATONIC DISCORDS
4L- ^J
.
-^ 1
ijhv^ JT] j -^^\
rr JT1 J J =1
|J J f" 7l
th* i> p * j P f
/ r r ' r r \
M.
r J
f ^ i J
J r=
I.J ^ j ^J
^
T=f
FREE COUNTERPOINT
337
Exercises on Free Counterpoint.
1 Treat the phrase given below in the following -way:-
ft) HtaJta it as a melody, beginning as indicated and wing dmtomc
enths or their inversions on every crotchet exceft those marked with an as
terisk.
(S> Harmonize it as a Bass in a similar way.
(4 Repeat it three times as a Qronnd-bass. The Imitations are given. Pill in
the missing parts, using occasional rests before the entries to heighten
their effect.
Allegretto
U)
888
DIATONIC DISCORDS
. Repeat this Ground-bass four times. The themes for imitation are given.
The student must find the places at which they enter. Each theme enters
once in the three upper parts, except the last which has two extra entries
which are not quite strict.
1
3 (Bass varied)
3. Repeat this Ground-bass three times. Add a short Coda. The figure given
for imitation at the third repetition comes twice in each bar, out in differ
ent parts.
Moderate
FREE COUNTERPOINT
J
339
The Ground-basses given in Section XV, Ex. 329 and Exercises 8-10 can
also be used.
4. Fill out the following according to the form shown in Ex. 389.
Allegro moderate T" ne by H.
* - Jn '
r-r r
J-
C.F.
Jjl. J =,
*===
M J ^ ^ J
,
Eircrr^
1 L
F r y -\
r (,j .
J J J J
(i ) Tteat theEe notes as pedals. (*> Th
840
DIATONIC DISCORDS
;j i i > * v i- 1 i 14-
' J. J-
*Ktu Qj
-if ' > r
(1)
f=f
W
6. Complete this in the form shown in Bx. 890 (five parts).
Con brio
Sops. 1 & 8 -
Alto
rr
r
m
Ten.
Bass.
d=U:
r^n-rrr
FREE COUNTERPOINT
341
IE
zr:
frQBJjJJ
m
F J
s
L f
^
342
DIATONIC DISCORDS
6. Write a short choral-prelude in the form shown in Ex.391. The C.F. with
its counter-melody, or descant are given below at (a) and (c).
1. Begin with the counter-melody alone, adding a Bass and one more part.
The style is indicated at (/>)
2. Combine the first half of the C.F. with the counter-melody. Here there
will be four parts, three in the accompaniment and the C.F.
3. Write a short interlude, developing the counter-melody and leading up to
4. The second half of the C.F. given at (c) with the counter-melody.
5. Make a coda or postlude, by returning to the beginning of the counter,
melody and adding a cadence.
Andante tranquillo
^
Ancient Irish ffymn Tune
(Copyright)
Counter Melody
M
m
FREE COUNTERPOINT
843
C.F.
HIM i r
Part 5 begins here
Double appoggiaturas are marked with slurs
7, Write imitations in the first form on this hymn tune in four vocal parts.
The themes are given, but not the points at which they enter. The length
of the prelude, interludes and postlude is indicated, but this plan need not
be strictly adhered to. _,, 7 , r _,. .
9 Illsley^y J. Bishop
(1685-17S7)
Theme
Answer
crr
Theme and Answer
( r if
844
8 Theme
Answer
>}!, r r f ^
^
4 Theme
*
Answer
i r irj f
8. Write imitations on this hymn tune in the second form in five parts, be
ginning as indicated.
~ _ York (from, Scottish Aalter 1615)
Second Soprano v '
,
Sop.
Alto
^
Ten.
JJ3JJJ
Bass
9. Write a choral-prelude in the third form on the following tune. The begin
ning of the counter-melody is given. The introduction, interludes and post-
lude may be in four parts; the rest in five.
Croft (1678-1727)
9 , > ,
I.
1 .1 1 MJ<
m
TT7Z
PART III.
CHROMATIC HARMONY
SECTION XVIII.
CHROMATIC PASSING NOTES.
265. Chromatic sounds are those which although foreign to the
scale do not change the key. The chromatic scale in Ex. 392 has no
influence on the tonality although it passes through every semitone,
for the triad of C beneath it neutralises any effect the foreign sounds
might have. From this primitive example it will be realised that
chords and chord progression have far more power in fixing tonality
than chromatic unessential notes, especially when these are merely
decorative. Ex. 898 sounds to be in C throughout if played reasonably
quickly, so that the chromatics give the impression of being ornamental.
But if the first bar were dwelt upon it might very well form a perfect
cadence in F (Ex. 894, bar 2). Even here it is the chords and not
the chromatics which settle the case, for it so happens that the alto
and tenor, as they fall through the semitones to the tonic triad, touch
a dominant seventh immediately before it, and this makes the harmony
of a perfect cadence the strongest factor in all music in fixing tonality.
Ex. 392
Ex. 398
346
CHROMATIC HARMONY
266. Chromatic passing notes are stronger and more definite when
they carry on in the direction in which they started till they reach their
destination and they should always have one (Ex. 395). But the
hum produced by running up and down a few semitones above and
below some harmony note, as in Mendelssohn's well-known Song
without Words, No. 34, is a conscious attempt to produce a desired
effect.
267. A great deal of the charm of chromatic passing notes and
chromatic appoggiaturas to be considered later is due to the fact
that they often produce in the course of their movement, by accident,
harmonies associated with other keys. In Ex. 396 (a), which only
plays round the dominant triad in F minor (Ex. 396 (b)), the triads of
A flat minor and D minor, and the second inversion of the dominant
seventh in D flat happen to be touched, all of them foreign to and remote
from the key of F minor. This imparts to the music a romantic atmos
phere and a feeling of mild adventure.
268. In working the exercises which follow, distribute the movement
as equally as possible between the parts, and analyse each passing
harmony made by the chromatic notes. In those exercises where it
is not given, think out the fundamental harmony .before arranging the
passing notes. Ordinary, diatonic passing notes can be used with the
chromatic ones. Obviously the distance between the harmony notes
and the pace of the moving parts will govern the situation. For instance,
a part moving at the rate of four notes to one will cover the distance of
a major third between two harmony notes if it moves by semitones
only. Therefore, if it has to cover a fourth, only one chromatic note
can be used, and there will be the choice of two (Ex. 397). The
movement of the other parts, the chords employed and the key must
be considered in settling which to choose. If the distance is less than
a major third there are several tricks to employ. For instance, the
part can mark time (Ex. 398), or it can dodge back one note or to another
note of the chord, and then proceed forward (Ex. 399). In the first
case it will cover a minor third, and in the second a whole tone.
Ex. 894
Ex.395
(weak.
(weak)
Jl
JJu
^
(stronger)
(stronger)
Ex. 396
rrt
*P
Ex. 396
CHROMATIC PASSING NOTES 347
Ex. 397 Ex. 398
Ex. 399
269. Chromatic passing notes may, of course, be unaccented or
accented. In cases where the latter are used they will appear before
the harmony notes given in Exercises 1, 2 and 3.
270. Chromatic harmony is more suited to instruments than to
voices, except when it is slow and the melodic intervals are not
augmented or diminished. Therefore, in order to use the easiest and
most flexible medium, some of the exercises are set for string quartet.
The elementary technique of these instruments can readily be learnt
from any text-book on orchestration.
271. Chromatic passing notes are very easy to write for there is
much more choice than when only diatonic notes are employed. Like
all things which cost little they are not of much worth, and if used
for long together and without an admixture of diatonic passing notes,
may sound very cheap and give the impression of much ado about
nothing. A shining example of this type of music is the Prologue to
Sullivan's " Golden Legend."
Exercises on Chromatic Passing Notes,
1. Add chromatic and diatonic passing 1 notes in the style of the first four
bars, i.e. one passing note between each change of harmony.
rif^
r
r r
r r r T r
: F=r=r :
r ."i: f
848
CHROMATIC HARMONY
o
A
te
i
. Treat this in the same way, but use two passing notes between the chords
where this is practicable. Write for piano.
Allegretto
8. Use three passing notes, as in the first four bars. Write for organ.
St. Anne
CHROMATIC PASSING NOTES
349
n^
r
w*s
r
r
r
j_
i w^
^^r
4, This Ground-bass should be treated as follows!" First, second and third
time, no shorter note than a quaver. Fourth and fifth, nothing shorter than
triplet quavers. Sixth and seventh, nothing shorter than a semiquaver. Use
the material given below. Write for strings in open score, the viola in the
Alto. clef.
Andante con moto
II
I * J bl J t
ViolaiT
'Cello
IV
350
CHROMATIC HARMONY
VII
SECTION XIX.
CHROMATIC TRIADS,
272. Chromatic triads are those which, although foreign to the key,
do not cause modulation because they are immediately followed by
some chord or chords definitely associated with it.
They are the healthiest of all the chromatic chords. They have
been in existence since the XVIth century and came naturally into
music with the increasing use of Musica Ficta (145). A classic example
is the opening of Palestrina's Stabat Mater (Ex. 400 (a)). The strange
emotional effect produced by this wonderful phrase has been obtained
by the same means over and over again by later composers right up
to our own times. A modern instance is given in Ex. 400 (fc), the last
five bars of the first of the " Mystical Songs," by Vaughan Williams.
It is best described by Pater's definition of the Romantic as opposed
to the Classic in art : " It is the addition of strangeness to beauty,
that constitutes the romantic character in art."*
Ex.400 (a)
Palestrina
F#T 1" ^
g~ r.
F=^
^ 'J 8 =1
Sta - bat
" r f
Ma - ter <
lo -
i
,0 -
ro - sa.
- - fl
jL4_
fx
^ ^
7^-
1 1
Ex. 400 ft)
Vaughan Williams
(Copyright)
text-books only allowed the
273. The XlXth century harmony
following chromatic triads :
(a) In both major and minor keys
(1) The major triad on the flattened supertonic.
(2) The major triad on the supertonic.
(b) In major keys only
(1) The minor triad on the subdominant.
(2) The major triad on the flattened submediant.
*" Appreciations" by Walter Pater (Macmillan).
entitled "Postscript " should be read.
The final essay on this subject
352
CHROMATIC HARMONY
The last two are borrowed from the tonic minor.
Nowadays any triad can be used chromatically. Let us consider
the older ones first.
274. The major triad on the flattened super-tonic. This
could easily be achieved in the modal period, as in shown in Ex. 401.
The later use with the chromatic chord followed by the dominant
(Ex. 402) involved the progression by a diminished third in one of the
parts forbidden in the XVIth century. It was originally only used
in its first inversion, and has always been known as the " Neapolitan
Sixth "-^supposedly because Alessandro Scarlatti and his School were
the first to use it. The reason why the first inversion alone was pre
valent until comparatively modern times is difficult to fathom. Ex. 408
(a) and (6) shows that use of the original position of the triad involves
no special difficulty.
It will be noticed that in Exs. 401-404 the chromatic chord is
always followed either by one of the primary triads tonic, dominant
or subdonunant or by a dominant discord. This prevents any change
of tonality. Even when a cadence is made in the key of the flattened
supertonic there is really no effect of change if it is followed im
mediately by some chord strongly characteristic of the original key
(Ex. 405).
This triad can always take tfie place of the ordinary supertonic
triad as may be proved by playing Exs. 401 and 402 with Bt] instead
of B[?, and all the rest without any accidentals. It produces, however,
a totally different atmosphere from that of the diatonic triad.
Ex.401
in
Ex.403
n=
nz
N
rt
t=J
. "-
-tjki
L"fJ |Q
-AJ 13
-CL- ^
e .
-e-
J
Ex.403
W
n
(
o
V I!
k|4 e
XT
e
H
8
ti i^:
^* *
TT
|p-e u.
*
Ex. 404
TTTl
..
CHROMATIC
TRIADS
Ex. 405
_fl 1 . ,.|
^
"v,
'^
i ^9
f l *~ v . l^lc
J-
*
1 ']
r ' r r '
353
275. The major triad on the super-tonic. This is another old
friend and has also been handed down from modal times (Ex. 244,
bar 26). The somewhat pedantic rule of the XlXth century harmony
book laid it down that it should be followed by some form of the tonic
triad (Ex. 406 (a) and (6)), or else a chord with the subdominant in it
to contradict the chromatic note (Ex. 406 (c) and (d)). But it really
causes no modulation even when followed by the dominant triad,
so long as the perfect cadence thus formed is not dwelt upon (Ex. 406
(e)). It will be observed that Ex. 406 (d) has an effective false relation
in it. The progression in Ex. 406 (c) is perhaps the weakest in all
music. In fact this chord has to be used most carefully in order to
escape from sickly sentimentality. The semitonal progression in the
alto in Ex. 406 (c) should be avoided, and the chromatic chord should
be followed either by an inversion of the tonic triad (Ex. 406 (&)), or
by some good strong discord in which the chromatic note is contradicted
in a different part (Ex. 406 (d)).
The chord of the sixth, which is the first inversion of the diminished
triad on the sharpened fourth degree of the scale, is first cousin to the
chord just discussed, and is followed in the same way (Ex. 407).
Exs. 401 and 402 are applicable to the tonic major if the C's are
sharpened, and Exs. 403 to 407 to the tonic minor if the E's are
flattened.
Ex.406
(i)
/ .> :
HI
_ r ^
-n ^
1 fr^j
fcV ' "i'
^ n
H
- J L
-e-
^ ft
~y ^^ o
-g't ' 'O
W)
101
IX it
Dei
EC
*tt=
Ex. 407
*E^=
^U.
AA
354
CHROMATIC HARMONY
276. The triads borrowed from the Tonic Minor. Two of
these are very common, namely, the minor subdominant and the major
triad on the flattened sixth degree of the scale. They are used to
take the place of the diatonic chords on those notes. The minor sub-
dominant may be very sentimental when it follows the major, as in
Ex. 408. The village organist loves it. But used without the descend
ing semitones (alto in Ex. 408) it is quite strong and often appears in
an extended final plagal cadence, as in Ex. 409.
Ex. 408
Ex.409
^
The triad on the flattened submediant is commonly used to form
an interrupted cadence. It interrupts the movement more surprisingly
than its diatonic relation. This can be heard by playing Ex. 410 with
and without the E and A flat in the last bar. It is often followed by
the subdominant minor triad. No triad with the diatonic sixth degree
of the scale in it sounds well immediately after it, one of the few cases
where a false relation is ugly. Ex. 411 sounds very crude with Akj
in the triad of F, but quite normal with A|j.
Ex. 410
NN
i
4-
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*=
=9*=
*L
i-
4^
Ex.411
^
277. Exs. 412 and 413 show that it is possible to use the chromatic
triads, major and minor, on every degree of the scale. These examples
give only one progression for each triad. Many others can be found ;
some are included in the exercises.
They can be used without incongruity so long as one or more of
the following are present :
(1) Smooth and conjunct part- writing. Augmented and diminished
intervals may cause ugly melodic progressions. Parts
moving in chromatic semitones should not turn back until
the progression is complete (266). See Exs. 412 and 413.
CHROMATIC TRIADS
355
(2) Some note common to the chromatic triad and the chord
preceding it, or to the chromatic triad and the chord fol
lowing it, or to all three (Ex, 412, lib m i n *> HI maj.,
IV# min., VI maj, Ex. 413, Ilfy min., III# maj., IIIJ
min., IV# min., VI min., VII|? min, VII maj.).
(3) A link-chord : that is, a chord which belongs either diatonically
or chromatically to the key the music happens to be in
and also to the key of which the chromatic triad is the tonic
triad. For instance, in Ex. 412, Ilty min., the link-chord
is the triad of F min., which is commonly connected with
the key of C chromatically (276) and with E flat min. In
Ex. 413, III# maj., the chord of the diminished seventh
on the fourth minim is to be found both in the key of the
chromatic triad E, and the key of C min.
After working out the exercises which follow, experiments should
be made with each chromatic triad (except those enumerated in (273)),
introducing and following them by other progressions than those given
in Exs. 412 and 413.
'. Roman figures denote the degrees of the scale.
Major Keys
II>min., | t Ell? maj.
"" "~ ' pA * _^
Hlbmin.
III maj.
Vl?maj.
T
*F
Vmin.
,
v
Ibmin.
VI
maj.
r
* T
^
J
I
H
I
--
^
I
J
:
^
-e-
^L
V 1
* Chord of the Augmented Sixth. See Section xx.
356 CHROMATIC HARMONY
Vllbmaj.
I
^
Vllmaj.
Ex. 413, Minor Keys, omitting triads shown in Ex. 44.
*V_ IllJtmaj. , | Illtfmin.
J
IMI
m
Vbmaj.
^
r
an
VImin.
^^-
ii 1 '^
Vljtmaj.
r
r
n
Vltfmin.
Vllkmin.
33=
VHrnaj.
CHROMATIC TRIADS
, VII min.
357
TT"
Efe
It has already been stated that these chords produce a mysterious,
remote and romantic atmosphere. Therefore they are somewhat
unsuited to the short exercises given here, which have no story to tell
or picture to paint. Nevertheless, familiarity with them and ex
perience in handling them is useful and necessary.
278. These triads, like all chromatic chords, are a very easy
means of modulation. They may be approached as chromatic triads
in one key and quitted as diatonic triads in another (Ex. 414, II}?
quitted as I). They may be approached as diatonic triads and quitted
as chromatic triads (Ex. 415, I quitted as lib), an d, thirdly, they may
be approached as chromatic triads in one key and quitted as chromatic
triads in another (Ex. 416, in which the first inversion of E is approached
as III maj. in C and quitted as lib in E flat).
Such extraneous modulations should be reserved for places in the
music where for some reason or another a vague tonality is wanted.
They could, for instance, be appropriately used before the return to
an original theme, for then the effect of the re-establishment of a fixed
key would be enhanced by the previous vagueness.
The chromatic treatment of the augmented triad is dealt with in
Section XVI.
Ex.414
jj^ *
BPP
^
Ex.415
Ex.416
m
^
358
Ex.417 ()
CHROMATIC HARMONY
m
I dim.
J
VI t>
j ij u ^
m
iEx.417(i)
rr
n
u
U. J.
^
f-r
^^
kmin.
I*naj. J j
M
i r i
1^ j j j=^=j
-in
J ,J'J J_!
aJ J J J |
f
^'^^ ^
-4^
*i
' \* I r
7 \ \
Bmin. i
r r
I'T 7 r T
r l r ^r n, :
-^-
Exercises on Chromatic Triads.
1 . Add Alto and Tenor
w=a^
- J^
F^=
Pc/r J
^ -
^^
1
j-i
t^J
m
m
(W
CHROMATIC TRIADS
359
. Harmonize the following bass twice. The first time introduce as many
chromatic triads as possible, the second time as many modulations as pos
sible, as in Ex. 417 (a) and (2jj). In bar 4 use Fjt the first time and Gl> the second.
8. Treat this melody in the same way as the bass in NP. 2. In bar 3 use Plj
the 1st time and E# the 2nd.
^~*IJ iiJ aJ)itJ^
'r r r r *r ^
' i ' ' ^
4. Add the missing parts, introducing as many chromatic triads as possible.
Ky - ri - e. Ky - ri - e e,- le - i -
Ky - ri - e e - le - i - son
51 - e
tt
ri-e
Chris -te e -
e - le
E^EE
i - son-
m
(in five parts with two Sopranos)
r r r ir^^
Chrig-te 'e - le
Chris 7 te e -
i - son, Chris -te e
son e -
son
360
CHROMATIC HARMONY
*j .
Ky - ri -
the Kyrie
adding a few bars
fo conclude it.
ft
5. Take the harmonies given as the basis for a short pianoforte piece. The
positions of the chords may be altered. The first two bars are complete.
Allegretto grazioso
I
A-
5^3
PPl
^^
6. Add ^nd Violin, Viola and 'Cello to this 1st Violin part, beginning as in
dicated. Introduce chromatic triads at the asterisks.
Andante tranquillo
. __ -
rrrrr
CHROMATIC TRIADS
361
^
fe
.<~^ rf^ 1
s
^=!
WTN. r
r hp r
m
-$
Md
B
$
fr crJsc. *
*
*
H^-J
* ' *
1. Add parts for; 1st Violin, 3nd Violin and Viola above this 'Cello part.
*The following chromatic triads can be included: I tt min., H !> min.,
H major, III aag., IV min., V \> maj., V b min.,VI t maj.,VI 'P min.,Vl maj.,
VII \> min. Begin as indicated.
Allegro vigoroso
CHROMATIC HARMONY
8. Add an Alto, Tenor and 1st Bass. The rest of the Psalm may also be set.
cresc.
Slow
i. jpp Soprano
j
j.
Out of the deep have I call - ed un - to Thee,
pU-^-i.-g=F
^
&=z
cresc.
rt=i
ki^e fa L r
dim.
n
Fft
p
=
spp
?Ji _ H^ f
Lord: Lord hear my
V-H r r ftr- J-
voice,
Lord h
ear_
\ u
'
1
V
my
1 "
o
voice.
r;^ 1
^z=
/L: 7. : p[
*
j:~*
~Tt
^
_ 1
10
">f
let Thine ears con-sid - er well the voice of my
cresc.
dim.
com-plaint,the voice. of my..
com - plaint.
m
dim.
of my
SECTION XX.
CHROMATIC DISCORDS.
(a) Classical Use
279. Chromatic discords are either chromatic triads with one or
nore added notes, or diatonic triads with added chromatic discords,
Taaking them into chords of the seventh, ninth, etc., or into chords of
:he augmented sixth.
Firstly the use of the natural, unequally tempered scale, and,
secondly the use of natural horns and trumpets in the orchestra, and
bhirdly convention, prevented the development of chromatic harmony.
Unequal temperament was practically killed by Bach, but chromatic
discords had been common long before his time. Even in English music
which, with the glorious exceptions of the great Tudor composers and
Purcell, lingered behind continental music, chromatic discords are to
be found in the late XVIIth century. They could only be used, how
ever, when the scale permitted it (Ex. 222) and enharmonic change
was impossible. Horns and trumpets which could play the chromatic
scale did not appear until Wagner's early days, but they were not
such a deterrent as the untempered scale, for they could be dispensed
with. Convention lingered even longer. Harmony text-books pub
lished towards the close of the XlXth century included no more
chromatic discords than those given below. Modem developments
will be spoken of later. It is essential to obtain a grip of the chords
given in (280) before the very wide door is opened to more modern
usage.
280. (1) Dominant discords. The dominant minor ninth and
thirteenth in major keys, and the major ninth in minor keys.
2. (2) Supertonic discords. A family of chords seventh, ninth,
etc. built up on the supertonic chromatic triad (275).
(3) Tonic discords. Another family having the tonic major
triad as a basis, including a flat 7th and major or minor 9th.
4. Augmented sixths. The Italian, French and German sixths
occurring on the minor 2nd and minor 6th of both major and minor keys.
281. Dominant discords used chromatically.
It will have been observed that the 3rd, 5th, 7th and llth of
dominant discords are the same in major and minor keys ; it is only
the 9th and 13th that alter (Ex. 312). The employment of the
minor 9th in major keys probably sprang from the chromatic use of
the minor subdominant triad (Ex. 418, in which it is combined with
the llth), and the diminished triad and its first inversion on the super-
tonic of minor scales (Ex. 419). Its treatment is the same as that
of the dominant major ninth (205).
The major ninth is also used in minor keys to harmonize the sharp
6th in the ascending melodic minor scale (Ex. 420). Here in two
examples it is combined with the 13th.
364
CHROMATIC HARMONY
The dominant minor thirteenth, when used in major keys, resolves
by rising a semitone to prevent a modulation to the tonic minor. It
is" usually written as a sharp 5th to avoid an accidental (Ex. 421).
It may have originated as a chromatic passing note and reached its
present state by elision (Ex. 422).
Ex.418
Ex.419
Ex.420
282. Supertonic chromatic discords.
These are notes added to the triad treated of in (275). All that was
said there applies here. The movement of the dissonant notes them
selves is the only new feature.
The supertonic seventh is simply a combination of the triad with
the chord given in Ex. 407. It is followed in the same way as that
chord, namely, by some progression strongly characteristic of the key
(Ex. 423 (a)), or by a chord which contradicts the chromatic note (6),
or, occasionally, by some chord which switches the music over from
the north, or dominant side of the tonic, to the south or subdominant (c).
The 7th can resolve in the ordinary way by descending one step,
as at (b) ; by remaining to be a part of the next chord, as at (d) ; by
leaping up a 3rd as at (a) (see also Ex. 407) ; or by rising one degree,
as at (e).
Ex.423
CHROMATIC DISCORDS
(6)
365
I
i
+ -
^m
(dl
Mozart used this chord (usually as the J given in Ex. 407) in a par
ticularly beautiful way. He obtained from it tenderness without sloppy
sentiment. In the sonata for piano in D, first movement (No. 18) it
occurs only in the fourth and last statement of the second subject, as
if he purposely kept the most expressive harmony for the end
(Ex. 424). Many consecutive descending semitones tend to senti
mentality in music, as has been stated in (275). Very ordinary chords
also tend to weaken it. Mozart's appoggiatura in the third complete
bar saves this example from banality. It is the dominant seventh
that is the culprit. Compare Ex. 425 with Ex. 423 (6) and (e). Here
the 9th is added to both supertonic and dominant chords. Even
when the semitonal movement is present, as in Ex. 425 (6), the pro
gression sounds strong. The resolutions of the 9th corresponding to
those of the seventh given in Ex. 423 will be found in Ex. 426. When
the 9th is resolved the 7th is free to move anywhere it pleases (Ex. 426
(c)) In fact, the root progression, II V I, has become so familiar
that it alone is often sufficient to produce a satisfying effect without
the actual resolution of dissonant notes (Ex. 425).
Ex.424
Hoiart
CHROMATIC HARMONY
Ex.426
The minor 9th of this chord is often used in major keys. It is
another example of a note borrowed from the tonic minor. Being the
3rd of the minor scale it might have a tendency to change the tonality
from major to minor were it not resolved a semitone upwards on to
the major 3rd of the scale (Ex. 427), or some other means employed
to maintain the key, as Ex. 428 (c). But this is not always the case
(Ex. 428 (&)). The minor 9th is often written as a sharp 8th in the
inversions when the root is not present. This saves an accidental.
If the common resolutions of the seventh given in Ex. 423, and of the
major 9th given in Ex. 426 are applied to it, as in Ex. 428 (a), (6) and
(c) we have three more resolutions of the diminished seventh, for in
its' inversions it becomes one. J. S. Bach used it very often, especially
at climaxes, as for instance in the coda of the organ fugue in C, Ex. 429.
After his time it was used for a similar purpose by others right down
to the beginning of the XXth century, as in Ex. 430 from Parry's
" Vision of Life " (1914). In this the A#, C# and fit] are appoggiaturas,
and the key is B minor. , . ^ ,,,.v
The supertonic eleventh has no chromatic note in it, as the llth
takes the place of the sharp 3rd. But it has a distinct family likeness
to the seventh and ninth (Ex. 431). The supertonic thirteenth usually
sounds very effeminate (Ex. 432).
Various combinations of 7th, 9th, llth and 13th are possible with
supertonic chromatic chords in the same way as they are with dominant
discords. There is no need to enumerate them here, for with the
experience gained in Section XV, together with what has already been
said in this section, their use should be an easy matter.
Ex.427
I
/
!L
428
(i)
(c)
=
r
CHROMATIC DISCORDS
Ex. 439
Ex.433
AJL
J,
r
283. Tonic Chromatic Discords.
Chromatic discords having the tonic as a root are not found so
frequently as supertonic discords. Their treatment is on the same
general lines, that is, they are followed by some chord or chords which
effectually dispel any sense of a modulation to the subdominant.
The flat 7th usually rises to the 3rd of the dominant (Exs. 423 (c)
and 428 (c)). It can fall if the music is switched over from the south
to the north side of the key, usually by means of some supertonic chord,
as in Ex. 433. At a cadence it is most often used in one of its inversions,
for the root-position of the chord would make the tonic arrive in the
bass too soon the music would get home, go a few yards away, and
then return always a bad effect unless there is sufficient length of
" coda " to warrant it (Ex. 434).
The minor ninth, if used with the 7th, rises a semitone when the
7th rises (Ex. 435). In its inversions, like other minor ninths, it
becomes a diminished seventh (Ex. 436). It will now. be seen that
with the resolutions given for this chord in Exs. 325 and 439, together
with enharmonic change, it is possible to resolve any diminished
seventh into any key, major or minor.
Ex.433 Ex.434
3C8
CHROMATIC HARMONY
Ex.435 V , Ex.436
284. The Augmented Sixth.
The three forms of the augmented sixth the Italian ( 6 ), the
French (4), and the German (s\ are shown in Ex. 437.
\3/ \3/
ft) i ..
(b)
(c) V
In classical harmony it was allowed on the flat 2nd and flat 6th
of major and minor scales ; but, like all discords, has a much less
restricted use now.
The Italian Sixth is simply the 1st inversion of the diminished triad
on the leading note with the bass inflected one semitone. Or, if it
is on the flat 6th of the scale, it is the chord shown in Ex. 407 with the
bass flattened.
The French Sixth is a 2nd inversion of a dominant seventh, or of
a supertonic chromatic seventh with the bass flattened.
The German Sixth on the flat supertonic bears a strong resemblance
to two chords. It has all the notes of the chromatic triad on the flat.
2nd of the scale to which is added an augmented 6th. But it is also
the first inversion of a diminished seventh with the bass flattened one
semitone. The German sixth on the flat submediant has a close
relationship with the chromatic major triad on that note, and the
diminished seventh shown in Ex. 428. Attention is drawn to these
resemblances and relationships for two reasons : (1) because they
show the use of the chord, and (2) because they indicate the way
modern composers have developed chromatic harmony. They show
the appropriate use of the chord, as very often either the chord itself
or its close relation are equally appropriate. Thus, if the German
sixth is substituted for the chromatic triad in Ex. 404 by putting Bq
in the tenor (Ex. 438), it is only the shade, so to speak, not the colour
of the harmony which is altered. In the same way the diminished
sevenths in Ex. 325 (6), (c), (d) and (e) can all be transformed into
German sixths by means of a slight modification of the part-writing
(Ex. 439 (a), (b) 9 (c) and (d)). The accidentals in brackets indicate
that by employing chromatic harmony these passages can now be
resolved either into a major or a minor key. This was not possible
in Section XV.
CHROMATIC DISCORDS
369
Ex. 438
/
t u J J i
1
^_^
(n o -
h^ fi-f-
g ^ 7
*
J J
f
'
Ex. 439
rt L ()
285. The ordinary resolutions of the augmented sixth on the flat
supertonic in its three forms are given in Ex. 440 (Italian), Ex. 441
(French), and Ex. 442 (German). These resolutions are applicable to
minor keys by flattening the 3rd in the tonic triad. Here they are
treated exactly in the same way as their cousins mentioned above.
The inversions of the Italian form are of no more use than the
chord of the diminished 5th and its 2nd inversion, for both the notes
are dissonant with the bass and therefore cannot be doubled. Thus
they can only be used in three-part writing.
If the German sixth in its original position is resolved directly
upon the tonic chord, consecutive 5ths result (Ex. 443). There is
BB
370
CHROMATIC HARMONY
nothing unpalatable to modern taste in these. They are one more
example of the effect of consecutives being nullified by dissonances
which distract the attention (203) (Ex. 316 (d)).
The chromatic notes in all three augmented sixths may be treated
as appoggiaturas. Two such resolutions are shown in Ex. 444. The
flat 5th in the German sixth is a free note in modern harmony
(Ex. 445 (a), (b) and (c)) and need not always descend one semitone
to resolve.
Ex.441
Ex.440
*e n H
$ R o
. ._ -
_*i e
J V *j
o n
fr~5 nr-
_ rl
~0 r
ti
> &-^~
"*J*feS "~~
*
^^
8
kx^
O r\
" o :
1 jj "** 11 1
U
~o -^
Ex. 442
Ex.448 Ex.444
4&
o
**
it
m:
Ex.
(!_
^m
^
,J
H3I
286. The three augmented sixths on the flat 6th of the scale are
shown with their common resolutions in Ex. 446 (a) Italian, (b) French,
(c) German.
As these chords are so nearly akin to supertonic chromatic discords,
mid as those shown in Exs. 440-442 are equally related to dominant
discords, it is quite natural that progressions like those in Exs. 423 (b),
426 (b) and 428 (b) should appear as in Ex. 447 (a), (b) and (c), where
one augmented sixth is followed by the other. At (b) the small bass
notes show how these chords can be regarded as ordinary sevenths
and ninths with chromatically inflected notes (see below). Similarly,
the process can be reversed and the dominant family can proceed
to the supertonic family (Ex. 448).
Modulation is effected by approaching a chord in one key and
quitting it in another (210). Thus the very common string of
sevenths given in Ex. 449 is made by approaching each seventh as a
dominant and quitting it as a supertonic. In Ex. 450 this type of
CHROMATIC DISCORDS
371
ultra-saccharine harmony is made one degree less cloying by sub
stituting augmented sixths for ordinary sevenths. In Ex. 451 the
German sixth on the flat 6th of C minor is quitted as a dominant seventh
in Db, and the tonic seventh in Dfc> as the German sixth on the flat
2nd of C minor.
3E
3E
3r:
3H
"
ti
Ex.447
Ex.448
i
\>QL
^
Ex. 449
Ex.450
U 1<8
1
oo k o Ii t
Ex.451
-r ir
^=^
r
287. The French sixth, like the augmented triad and the diminished
seventh, can be made to do duty in more than one key by means of
enharmonic change. Ex. 452 shows that the French sixth on Dfr has
the same sounds as that on G. As the French sixth on Dfr may be used
in the keys of C major and minor, or F major and minor, and that on
G rjaay be in the keys of F# major and minor or B major and minor,
it will be seen how readily modulation can be made from one of the
first four keys to one of the second by approaching the French sixth in
one key and leaving it in another.
Ex. 452
3712
CHROMATIC HARMONY
288. The French sixth and the augmented triad are the only chords
which will fit with the " whole tone scale" (Ex. 453). They were
cunningly used for this purpose by Debussy. But even his music
evidences the harmonic limitations of this very mechanical scale, so
that its use was but a short-lived fashion,
289. It need hardly be said that the best notes to double are the
3rd in the Italian sixth, the 4th in the French and either the 3rd or the
5th in the German.
Ex. 453
I
m
Exercises on the Classical use of Chromatic Discords.
Theme.
Allegretto
CHROMATIC DISCORDS
373
1. Variation I. Supply the inner parts.
Andante congrazia J-=gJ.
. Variation H. Supply the lower parts in the style indicated.
Tempo della Tema
r=4
dzft
^m
3. Variation III. Sqpply the upper parts.
^- -^
3
T
tat
874
CHROMATIC HARMONY
4. Variation IV. Add the lower parts
Andante
^
cresc.
dim.
5. Variation V. Add the upper parts. Use Bfc as an inverted pedal^ointthrou^i-
out the first four bars, Dt> in bars 5 and 6, Bk from bar 6 to bar 9, and
F in bar 10.
Grave
cresc.
*An Inrerted pedal-point is a note (uually the tonic or dominant) held on in some part other
than the bas. Like an ordinary pedal-point it mut be part of the harmony at the beginning
and end of its duration.
CHROMATIC DISCORDS
375
6 Variations VI and VTI must be original work. Suggestions are a Sarabande
in Bi> minor, beginning something like this:
R.I. L H f
7 and an Allegro developed from the
8rd and 4th bars of the theme, two bars of the variation equalling one of the
theme.
Allegro ^
.! jr-vrHH . F
This most end with a cadence in P major leading to the Finale
8. Finale. Complete this according to the instructions given.
Allegro con brio (8 part Fughetta)
Subject in Bass
Counter-Subject in the middle part
Add a free part on the top ending thus:-
376
CHROMATIC HARMONY
C.8. in Bass
S. in middle part
Free part on top, ending thus:-
Continue this episode for a few
bars, leading to an entry of the
Answer in the Bass in D minor modulating to G- minor. Counter-Subject in the
top part, middle part free. Follow this with an episode beginning like thia:-
leading to an insistent
dominant 7th in El> which
turns into an augmented 6th on the submediant of D minor heralding the en
try of the inversion of the Subject in the top part and a modified form of the
Subject in the bass. Add the middle part.
their entirety
Episodes are portions of a composition in which the the*
>ntirety, but the material used may be taken from the themes.
which the themes do not appear in
CHROMATIC DISCORDS
377
Another short episode leads
to the following :-
allarg. a tempo, fiiu tranq uillo
Continue this stretto at the
octave over a tonic pedal, and
add a few bars of Coda, ending pianissimo.
9. Add nd Soprano, Alto and Tenor to the following using the chords in
dicated, (1) = Discords "borrowed from the tonic minor.
() m Super tonic chromatic discords.
(8) =r Augmented sixths.
(4) = Tonic chromatic discord.
1st SOP.
p j .,
ft f j * f \
i r n r Pi -:^
BASS
^ m ? T rt
==H
) \ 1 1 "J^
LJ
^H=
(D
(i) <)
378
CHROMATIC HARMONY
(6) Later Developments.
290. It will now be realised that the augmented sixth is a seventh
either of the dominant type or diminished with one note inflected
downwards one semitone. The two sevenths of the dominant type
in common use in classical harmony were those on the dominant and
supertonic. The two diminished sevenths most frequently met with
were the first inversions of the dominant and supertonic minor ninths
with the roots omitted. Therefore the two augmented sixths
originated by inflecting the notes of these chords. Naturally, when
discords on the other notes of the scale began to be used, (203) it occurred
to composers to inflect chromatically, either upwards or downwards,
one or more of the notes of these chords. To tabulate every possibility
of such inflexions is beyond the scope of this book, and would serve
no purpose. General principles can be explained and a few particular
cases instanced by way of illustration. The rest must be left to the
student.
291. Sense of key still influences the use of these harmonies. That
is, the ear dictates that a chromatically inflected note will have a
tendency to proceed in the direction in which it has been inflected a
flattened note downwards, a sharpened note upwards. If sense of
key did not exist, there would be no such tendency, for inflected notes
are inflected from their position in a recognised scale. By the time
this stage of the study of harmony has been reached such inherent
tendencies in the notes of a chord will already have been realised, and
that such tendencies depend on sense of key.
292. It is not always the established key which determines the
progression of the chromatic discords, however, for very often they are
the pivot by which a change of key is made. Frequently, as has been
shown (210), they are ambiguous in the equally tempered scale. In
these cases it is the new key which will govern the progression, and
this new key exists only in the composer's imagination. But it does
exist, even if the actual time spent in passing through it is but transitory,
For instance, no one can say, on first -hearing, whether the D[? and fit]
and the Bbb and G in Ex. 454 are augmented 6ths or minor 7ths.
The composer alone knows what is going to happen. It is his intention
to start in C major, proceed to a French sixth on the flat supertonic,
resolve this into A|j, proceed to another French sixth in that key,
convert this into a dominant seventh in D by inflecting the 4th upwards,
and resolve it normally. Having been reared to a sense of tonality
of some sort major, minor, modal and having to listen daily to
CHROMATIC DISCORDS
379
music written with that sense, how can he (or anyone else) suddenly
divest himself of it ? Moreover, if he did he would lose one of the
greatest means of contrast and variety in music, and upset the basic
ideas of form and symmetry one theme in one key contrasted with
another theme in another key.
Actually, if some such modulation as that in Ex. 454 were included
in a composition, the composer would not spell it out and analyse it
in his mind any more than an artist would work out what would be
the result of mixing two colours. As to how much the technical side
entered into the process would depend on the frequency with which
the composer was in the habit of writing similar passages. Such
modulations are written because the effect to be obtained is what is
wanted at the particular point reached in the composition when con
sidered from the point of view of the context, or even of the composition
as a whole.
293. The augmented sixth on the subdominant in Ex. 454 is an
instance of the trend of the modern use of chromatic discords. This
resolution is but a very short step from the ordinary one in F minor
(Ex. 455 (a)), or from the inversion of the dominant ninth in Ex. 455 (b),
Ex.454 Ex.456
(o)
i
^
po=
n
f
294. As a commencement to the study of these chords the chromatic
triads in Exs. 412 and 413 may be converted into sevenths by^the
addition of either the major or minor 3rd below, or the major or minor
7th above the roots of these chords. A few are shown in Exs. 456
(major triads with added notes) and 457 (minor .triads with added
notes). These adcjed notes are printed black. Incongruity can be
avoided by the same means as for the chromatic triads (277) and by
observing whether the inherent tendency of the notes is to rise or fall.
Ex.456
(N
11 f
*X
=
r
^
.. J
^f r
i J L J
H
^i
b=
o
3F
in
: ^8 8
V*
^
r *r
"f
dZ 1
CHROMATIC HARMONY
fe
SE
Further Exercises on Chromatic Discords.
10. The accompaniment to this Welsh Melody ('The Dove') is treated in such
a way that many of the notes may be chromatically inflected. Insert
accidentals wherever you think this may be done without making the
music sound either lugubrious or sentimental. Generally speaking the
sharpening of 3rds and the flattening of 7ths makes the harmony smooth
er but weaker. The accidentals in brackets in the first two bars show
the idea.
T oice Andante
I'Wi J Jf
CHROMATIC DISCORDS
381
382
CHROMATIC HARMONY
11. Complete this Scherzo by adding the missing parts, Write an original
Trio, with a bridge passage leading back to the Scherzo.
Scherzando
Violin I
Violin I.
arco
CHROMATIC DISCORDS
383
Viola
pizz
SECTION XXI.
CHROMATIC APPOGGIATURAS.
Chromatic Counterpoint.
295. Appoggiaturas have been explained in (180) and (244). A few
more remarks about t their use, particularly their chromatic use, will
be helpful. They abounded in the music of the latter half of the
XlXth century, when the opulence and luxury of the time pervaded
the art. Composers seemed to forget that the supreme artist achieves
his end with the fewest notes. But in all ages the great masters have
succeeded in spite of the defects or limitations of the idiom of their
time. Wagner and others have left us a heritage of great music even
though it has very little economy. At that time composers denied
themselves nothing to deck out their message in the richest garments.
Appoggiaturas were one means to that end.
296. They may be divided into two classes :
(1) Those which decorate the passage work.
(2) Those which colour the harmony.
The first kind move against a sustained chord, as in Exs. 458 and
459. The second are often more weighty, so that there is time for the
rich colour of the harmony to make its due effect. In many cases two
or more parts have appoggiaturas simultaneously. Ex. 460 shows two
together in bar 3, whilst in bars 3, 4, 12 and 13 of Ex. 461, there are
three. Ex. 462 has numerous instances of appoggiaturas used to
decorate the passage-work and to colour the harmony. Ex. 463 (a)
shows an appoggiatura used with a chord, one of the notes of which
has been chromatically inflected. The simple form of the progression
is given at (b).
297. When appoggiaturas were first employed they had a greater
stress than the notes upon which they resolved. From the examples
given it will be seen that in more modern times they may be either
accented or unaccented. In Ex. 458 the second of the two notes forming
the double appoggiatura comes on the beat. In Ex. 459 there are
three cases of double appoggiaturas, the accentuation being as in Ex. 458
in the first one, and the opposite way in the last two. In both these
examples the $ame chord is sustained during the appoggiaturas. But
in some cases the appoggiatura is an anticipatory note. This is fre
quently so with the double appoggiatura, the first of the two decorative
notes occurring before the change of chord and the second afterwards.
In Ex. 462 this type is marked with a cross.
298. Ex. 464 is an attempt to show the infinite number of ways of
decorating a simple harmonic progression with appoggiaturas.
299. Technically there is nothing much to say about their use.
It is simple to calculate the amount of dissonance they will create.
It is easy to arrange them so that they will provide flowing parts.
CHROMATIC APPOGGIATURAS
385
300. The aesthetic side must, of course be left to individual taste.
Chromatic appoggiaturas can create beautiful and unexpected harmonic
colour. They can also be mawkish. They can be used legitimately
in passage-work when they are part of the thematic material. They
sound fussy and illogical when they are included to distract the listener
from the poverty of the music.
Ex.458
l>L.Slow. t rit
'Naclitigall? Song Op. 97. N9t, Brahms
' Voice
Piano
t
fttng
-F-*
Ex.469
Allegro
Tone Picture Op.3. N?l. Qrteg
Ex. 460
Lento e languido
386
CHROMATIC HARMONY
\atm.
dim.
I -
f
Ex.463
Overture to Die Meistersinger Wagner
Moderate
CHROMATIC APPOGGIATURAS
387
Ex.464
?.
Single in one part
^
T
Anticipatory
Single in two parts
"With chromatic passing notes
Double in one part
IJ , J>J-
^-J-^^-. LJ 1 1 fcj
$ f J r
i ?*
-k H Jr
4
-* W-
^r r
1 =*= pC-
p J
Anticipatory
In two parts
^
888
CHROMATIC HARMONY
Exercises on Chromatic Appoggiaturas.
Decorate the chord progressions given below with chromatic and dia
tonic appoggiaturas on the lines of Ex.464.
J.
:! :
r^ i 1
<
,L
LAJL
p
Iff 1
-Jf 1
^^
-4 T+
^^
a -I
^
4. Write a piece for piano in which the left hand sustains the harmony in
arpeggios, whilst the right hand plays arabesques, introducing chromatic
appoggiaturas, as in the given bars. A suggested chord-progression is
given, together with the first few bars, but these need not necessarily
be adhered to, nor need the piece finish in 80 bars.
Allegretto con grazia
CHROMATIC APPOGGIATURAS
389
Suggested harmonic frajne-work
390
CHROMATIC HARMONY
5. Write a Schei2o for string orchestra as follows:-
Violins I
^ Allegro molto
T f .-.- r.-.- -
if r r i
f r f
Violins II
- L 1 f
j j. .
i r ^
J J r
"f ''f ~
if r r
Violas
IJ J ^
/?pizz.
j J P
J r
r r r
-F 1 i
r f *r j
^J L,, . ' 1
\f F r
'Cellos
): . > H p
j * r
/>pizz.
i y *
-i \- i
+ i i
I y k J r
/pizz
C. Basses
J * *
t^
/pizz.
la=i
^
^
Violins I
Add the 2nd Violin and Viola
Bassi
jj
CHROMATIC APPOGGIATURAS
391
- -
rr -9 -
err *-
cresc.
cresc.
m
Continue this repetition of the
first tlneme for about 5 bars,
ending in G minor instead of D rum
or- Bars 4 and 5 axe like tkis;-
392
CHROMATIC HARMONY
I&II
Violins I
Divisi
III
Violins II
Divisi
24 25
con sordini
Second theme
pizz.
&
=i=i
PP
CHROMATIC APPOGGIATURAS
393
Continue this second subject for
about 20 bars, finisMng in F. toe
, surging imprecations of the nnmuted instruments die away a few barf
before the end.) Then make a convincing return to the first theme.
The following bass may be used:-
m
arco semfre cresc.
Make a short recapitulation and then a coda, in which a brief refer
ence to the second theme in G major can be made. Follow this with a
Presto ending, jjp.
394
CHROMATIC HARMONY
Chromatic Counterpoint.
301. A few exercises are appended wherein the chromatic harmony
of the three previous sections and the present one are applied to counter
point.
302. Only one point needs explanation, namely, the answering of
fugue subjects containing notes foreign either to the tonic or dominant
keys. These notes may be of two kinds : (1) those which cause a
modulation to some attendant key other than the dominant ; (2)
chromatic passing notes and appoggiaturas. To answer such fugue
subjects the following methods are adopted :
303. If the subject modulates, but not to the dominant, it is simply
transposed in the usual way a 5th higher or a 4th lower. Ex. 465 (a)
modulates to the subdominant and the relative minor. The answer is
shown at (6), where the subject is transposed a 4th lower except the
first note (256).
304. If the subject modulates to the dominant as well as to some
other key or keys, it must be divided at some convenient place into a
tonic group and a dominant group. The tonic group, together with all
transitory key changes, is transposed a 5th higher or a 4th lower. The
dominant group is raised a 4th or lowered a 5th. In Ex. 466 (a) the
tonic group has a modulation to the subdominant and its relative minor.
In the answer (6) this is transposed a 4th lower. The dominant group
has a modulation to its relative minor ; this is transposed a 5th lower.
Ex. 465
Ex. 466
J J i J
r r rr J i
li 1 1 I I PI
CHROMATIC COUNTERPOINT
.395
305. Appoggiaturas, single and double, and other unessential notes
being merely decorative, do not affect the answer the subject is
answered without reference to them. Ex. 467 (a), if stripped of its
decorations, becomes as, at (6). The answer to this is (c), which if
redecorated, will appear as at (d). '
Ex. 467
(*).
J I|JJ f
I
Exercises in Chromatic Counterpoint.
Write answers and counter-subjects to the fugue -subjects given below and
also to Exs. 465-7.
1
Violin I
Allegro con spirito
A j. ^""**
* (Answer for 2nd Violin)
Viola Allegretto con grazia
1)11 nH
ll
896
CHROMATIC HARMONY
Piano Allegro moderate
'
The counter-subject can be in double counterpoint at the 15th.
4
Piano
Allegretto
The counter-subject can be at the 15th.
Bass Voice
Moderate
6. Write a choral prelude for organ and voices in unison on the model
shown in Ex. 890, beginning as under.
Voices
Maestoso
CHROMATIC COUNTERPOINT
397
i " i n^
IT
7. Write a three-part Invention for pismo on the triple counterpoint given
below. Either follow the plan laid out, or work out an original plan.
398
CHROMATIC HARMONY
Plan for Exercise 7. The numbers in columns 3, 4 and 5 refer to the three
subjects of the triple counterpoint*
Bars
Keys
Upper P^rt
Middle Part
Lower Part
Remarks
1-8
8-5
5-7
7-9
9-11
11-18
18-15
15-17
17-18
21-24
24-26
26-29
Cmin.
Gmin.
Gmin.
to
At
At
Ak-Ek
Ek
Bt
Cmin.
Cmin.
Cmin.
Gmin.
Cmin.
1
8
2
1
1 inverted
and
modified
1
2 inverted
2
2
1
1
8
8
8 modified
1 inverted
8
Rest
2
8
2
2 inverted
1 in verted
8
1
i tl< n j5pT>
*f?lrtr
on [ / ft. f U U""4d P
Chromatics to be modified to fit
the major key.
Episode J? Lr -'( - m p *
r jra-
^V], y y^gTt^"**^*^"
Closing group leading to perfect
cadence in Ek End of first part.
i itfyhy H ![ y :....* ',LJJ/ -
r r - t y.
B P l8 ^ de jk|> (, I '[< p LJ
Make the major 8rd of Gl> into
the minor 3rd of G minor.
Closing group as at bars 18.15,
but now in C minor.
CONCLUSION.
Practice must always be ahead of theory. It would be impossible
to investigate here all the many developments of contemporary harmony,
for it would confuse the majority of students and make this book of
unwieldy size. The following points, however, may be of help.
In no art has there ever arisen a genius who upset all previous theory
and practice. All the progressive composers have thoroughly in
vestigated the work of their predecessors before they made fresh dis
coveries. Their innovations were logical developments founded on
that which had already proved itself.
No new tendency can better the art of music which deprives it of
contrast. Of all the arts it has the most variety. It has infinite
contrasts of time, pace, rhythm, compass and dynamic range, in the
degrees of consonance and dissonance, in key changes, and the contrast
of diatonic with chromatic harmony. Through these wonderful
changes it expresses every type and degree of feeling. On these it
lives and moves and has its being. Anyone who would rob it of variety
is doing it harm. The fact that discords are more freely used in these
days is no reason for depriving us of concords. Though modulation
and chromatic harmony are so natural to us, we must not lose all sense
of key relationship. We arc not harnessed to one bar-length throughout
a composition as the classical composers were, but we must use that
freedom aright : it would be silly to allow it to make our work vague
and formless.
Finally, the student will find that force brings ugliness in its train.
If there is an urge to write music to express deep feeling, then the
result will certainly be more beautiful than when composition has to
be slogged at to pass an examination, or when a composer forces himself
to write in an idiom which is unnatural to him.
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